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How to find the Units Digit
by Total Gadha - Tuesday, 9 October 2007, 03:25 AM
  cat
Re: How to find the Units Digit
by Natasha Sachdeva - Thursday, 18 October 2007, 01:29 AM
  I am a new entrant to TG group .Beautiful! is what I have to say for all the articles I have read till now. Thank yoy TG sir
Re: How to find the Units Digit
by upadrasta jagadish - Thursday, 18 October 2007, 09:01 PM
 

Dear TG,

I could not understand, how U solved the final problem.

Could U please explain.

ThankU

Jagadish

 

Re: How to find the Units Digit
by Aash --- - Saturday, 3 November 2007, 02:19 AM
 
its simple we know that when f(x-a ) is the factor of f(x) then f(a)=0

similarly here
         17 
     13
  11
7
 units digit will be remainder of 11^13^17
here 11 can be wrutten as 4*3-1
let x=4
(3x-1)^13^17/x
will be x=0
(-1)^13^17
which will be -1
or 3
so units digit will be 7^3=3
Re: How to find the Units Digit
by Aash --- - Saturday, 3 November 2007, 02:20 AM
 
its simple we know that when f(x-a ) is the factor of f(x) then f(a)=0

similarly here
         17 
     13
  11
7
 units digit will be remainder of 11^13^17
here 11 can be wrutten as 4*3-1
let x=4
(3x-1)^13^17/x
will be x=0
(-1)^13^17
which will be -1
or 3
so units digit will be 7^3=3
Re: How to find the Units Digit
by mohil joshi - Wednesday, 9 July 2008, 12:21 AM
 

Awsome dude ! Wish I was in Delhi. Could you plz explain the last problem.

Thanks

Re: How to find the Units Digit
by Divya Aggarwal - Thursday, 10 July 2008, 09:56 PM
  The last one can it be explained again through more examples ..please smile
Re: How to find the Units Digit
by vishal goyal - Saturday, 19 July 2008, 12:17 PM
  FUNDOO
Re: How to find the Units Digit
by shuchi jain - Sunday, 20 July 2008, 11:26 PM
 

hi..article is good

bt can u tell me hw find the unit digit of 77^7^7^7^7^7^7......

plz do reply.........

 

Re: How to find the Units Digit
by TG Team - Monday, 21 July 2008, 04:59 AM
  Hi Shuchismile
77^7... = (8 - 1)odd = 4k + (-1)odd = 4k - 1 = 4k + 3.
=> 74k + 3 = 73 = 3smile
I hope i've not made any mistake this time.
Re: How to find the Units Digit
by Mukesh Kumar - Monday, 21 July 2008, 09:12 AM
  its good stuff....
Re: How to find the Units Digit
by Rohit Pathak - Tuesday, 5 August 2008, 03:05 PM
 

Hi Sir,

Could you please explain me how the last prob was solved, the solution mentioned is not getting clear to me esp the 11=12-1-> Remainder[11 odd]= Remainder[(-1)odd]= -1 = 3 thing.

Please explain the same to me.

Thanks and Regards,
Rohit

Re: How to find the Units Digit
by Anubhav srivastava - Tuesday, 5 August 2008, 10:21 PM
  Hi,

Can anybody tell me how to get the unit digit of number 7^8^8^....??? I want to differentiate it with the solution provided for question 7^7^7..., in which power is an odd number.


Thanks
Anubhav
Re: How to find the Units Digit
by vikas bains - Tuesday, 5 August 2008, 11:40 PM
 

Hi Rohit,

let me try to explain this:

in the example we are actually trying to find out the last term of the power of 7.

the basic funda is to check its (i.e. 7) cyclicity. This means 7 repeats itself as a last digit if it is multiplied 5 times. Hence its cyclicity is 4.

Which implies last term of 7^4, 7^8, 7^12, 7^16 is = 1, this can be read as last term of 7^4x is 1.

so we will try to make the power as a multiple of 4.

now, consider 7^11. this can be written as 7^(12-1). here we will try to write 11 as multiple of 4

this can be done as 4x2 + 3 or 4x3 - 1, first one

i.e. 7^(4x2 + 3)^odd is difficult to calculate.

hence we use 7^(4x3 - 1)odd, because we know (-1)^odd = -1.

we have done this because multiple of 4 will always give 1 and rest of the term became (-1)^odd, which is -1.

now for any number (say 4) if we say that the remainder is -1, then this means, if we would had added another 3 to divident the remainder would had been 0 when divided by 4.

7^11 or 7^(4x2 + 3) = 7^3 = 3

so, 7^11 or 7^(4x3 - 1) = 7^3 = 3

similarily, if we had a situation 7^10 = 7^(4x3 - 2) which is equal to 7^(4x2 + 2) = 7^2 = 9

and -3 = +1 which will give 7 as the last term, so on..

Hope this had help you?

 

 

Re: How to find the Units Digit
by Dipanjan Biswas - Wednesday, 6 August 2008, 02:19 PM
  Hi Vikas I got an easier approach
7^8^8^8...
Now as the power of 7 is divisible by 4 so the power is in 4k format.
7^4k gives unit digit 7..

So 7 is the answer..

Cheers
Re: How to find the Units Digit
by sharon koshy - Wednesday, 6 August 2008, 06:21 PM
 

HI DIPANJAN,

I THINK VIKAS GAVE THE ANSWER TO 7^11^13^17 AND NOT 7^8^8^8..........AND THE UNIT DIGIT OF 7^4K IS 1 AND NOT 7..........PLS CORRECT ME IF I HAVE MISUNDERSTOOD

BYE

Re: How to find the Units Digit
by Dipanjan Biswas - Thursday, 7 August 2008, 03:16 AM
  Yes you are correct with both answers..smile
Silly mistakes are integral part of my QA. angry

Another eye opener..
Thank you Sharon

Re: How to find the Units Digit
by sharon koshy - Thursday, 7 August 2008, 12:57 PM
 

you r most welcome dipanjan..........................

 

Re: How to find the Units Digit
by sharon koshy - Thursday, 7 August 2008, 12:59 PM
 

hi vikas,

thankyou for the explanation....................i actually understood the solution only after reading your explanation.............

Re: How to find the Units Digit
by vikas bains - Thursday, 7 August 2008, 09:42 PM
 

Hi Sharon,

Thanks for the response and appreciation, its good to hear that you understood my explaination. Thanks again

Re: How to find the Units Digit
by shashank tandon - Friday, 8 August 2008, 05:35 PM
  Hi kamal,
             i have one query with ur soln i.e
suppose k=1111
then 4*1111 = 4444
now 4444+3 = 4447
which implies last digit is 7
Re: How to find the Units Digit
by Prasad Satyam - Saturday, 9 August 2008, 11:57 PM
  thank you sir for wonderful information
Re: How to find the Units Digit
by jatin mehta - Friday, 22 August 2008, 11:01 PM
 

na na.

4447 is exponent . so our no. is 7^4447. and as explaind in theory unit digit  will be that of 763. i.e. 3 cool

Re: How to find the Units Digit
by Mukesh Kumar - Friday, 5 September 2008, 10:48 PM
  Can anybody tell me how to find out the unit digit of 7^18^18^18 using concept used in last example of theory...
Re: How to find the Units Digit
by Sibsankar Dasmahapatra - Monday, 8 September 2008, 01:05 PM
 

Hi Dipanjan

                    7^8^8^8....unit digit should be 1.....as 8^8^8...(4.2+0)^8^8...gives the reminder 0 once divisible by 4 .

           so 7^0...1 ans..

Re: How to find the Units Digit
by Sibsankar Dasmahapatra - Monday, 8 September 2008, 05:50 PM
 

Hi Mukesh

                      You can solve this problem by the method of "last two digit find out".....18^18..last two digit..76..now 18^76...last two digit..24....so 7^24...unit digit 1 ...ans ..

 

        am i correct???

                

Re: How to find the Units Digit
by Sibsankar Dasmahapatra - Tuesday, 9 September 2008, 04:50 PM
 

hi ..

          Today i have got another way to solve the problem.....remainder 18^18^18 , once it is divisible by 4 ...(4*4 + 2)^even number ....so it will be 2^even number....then....atlast it will be..0...so 7^0 ...will be 1...ans will be 1..I think now u are clear abt this..

          Thanks

         Sibsankar

Re: How to find the Units Digit
by Rohit Sharma - Tuesday, 9 September 2008, 06:08 PM
 

Hi Dipanjan

 

This is clearly mentioned in the theory abve when 7 is raised to power which is multiple of 4 gives units digit 1

Re: How to find the Units Digit
by nimish vikas - Friday, 12 September 2008, 09:37 PM
  dipanjan and sharon
u both have understood vikas wrongly.
it would help u to read it again

Re: How to find the Units Digit
by srini r - Wednesday, 17 September 2008, 10:56 AM
  Kudos TG you Rock!
Re: How to find the Units Digit
by Rangesh Sridhar - Tuesday, 23 September 2008, 01:57 PM
  Hey,
My Explanation is something like this : let us try and find a pattern for the remainder of higher powers of 11 divided by 4.
it so happens that all even powers of 11leave a remainder of 1 and off powers leave a remainder of 3 when divided by 4.  now, 13pow17 is an odd number, so it leave a remainder of 3, Therefore
         17 
     13
  11  = 4k+3.
Now,

     17 
     13
  11   (4k+3)
7 = 7
to find the last digit of this number divide it by 10, and the answer that is obtained is 3.
Re: How to find the Units Digit
by sushmita kolhapurkar - Tuesday, 23 September 2008, 10:12 PM
 

hi sibsankar

can you explain how 2^even number will give 0.

thanks

Re: How to find the Units Digit
by sriram siddarth - Thursday, 9 October 2008, 07:51 PM
 

can you explain how 2^even number will give 0.

thanks

Re: How to find the Units Digit
by shantanu chaubey - Friday, 10 October 2008, 01:59 AM
  Hi...TG, i know it's not the right place to ask this query but as i'm new to this site, i can't find any suitable forum.....Actually some days back i visited this site and found one Geometry quiz which contains lots of quesions, but now its missing...Plzzzzzzzz can someone give me the link........quick response will be appreciated.....
Re: How to find the Units Digit
by Mohammad Hussain - Saturday, 11 October 2008, 06:09 AM
  Hi.......... can any one post chapter wise questions for practice. to utilize the given methods.

Regards
Hussain
Re: How to find the Units Digit
by Puneet Satija - Monday, 13 October 2008, 12:15 AM
 

Dear TG

I tried to solve the last question using what i have learnt from this write-up.To find the units digit of

71113 raised to the power 17

First I found out the units digit of 711 .   711=73 Therefore the units digit 711=3 .Now 71113= (A number with units digit 3)13 .Therefore units digit of this number is same as the units digit of 313 Which is equal to 3.Further the units digit of (a number with units digit 3)17 is again 3.

Finding it hard to see my mistake.Please correct me if i am wrong

Regards

Puneet Satija

 

Re: How to find the Units Digit
by Software Engineer - Monday, 13 October 2008, 02:48 PM
  Puneet,

7^11^13^17. Now, find the remainder when power is divided by 4.

[11^13^17] mod 4
= [(12-1)^13^17] mod 4
= [(-1)^13^17] mod 4
= -1 mod 4 (-1 raised to odd power gives -1)
= 3 mod 4

Thus, unit digit of 7^11^13^17 = unit digit of 7^3

7^3 ends in 3.

- SE

Re: How to find the Units Digit
by Sibsankar Dasmahapatra - Wednesday, 15 October 2008, 05:14 PM
 

Hi susmitha

                         If you divide 2^even by 4 ; remainder will be 0; have u got it....

Thanks

Re: How to find the Units Digit
by gunjan talwar - Wednesday, 12 November 2008, 10:17 AM
 

hey...

remember the formula 4k+(-1)odd or even

if you have an:

  • odd power e.g. 7

we get 4k+(-1)7=4k-1    ..........(1)

  • even power e.g. 8

we get 4k+(-1)8=4k+1   ...........(2)

if we notice the powers of seven then we notice that the unit's digits are repeated after every 3 turns.like

7^1=7

7^2=49(unit's digit = 9)

7^3=283(unit's digit =3)

7^4=1981(unit's digit=1)

7^5=13867(unit's digit=7)

whatever value is when placed in eq. (1) and (2)

we get unit's value  to be either 3 or 7.

Re: How to find the Units Digit
by vikas sharma - Monday, 16 February 2009, 05:44 PM
 

can u pls tell if at place of 11 there is 14 in question

 

Re: How to find the Units Digit
by Seshu p - Tuesday, 24 February 2009, 10:01 PM
  14 is even. So, 14^(any number greater than 1) leaves a remainder 0 when divided by 4.

So, required units digit: 1

Re: How to find the Units Digit
by vikas sharma - Wednesday, 25 February 2009, 04:34 PM
 

Thanks seshu p

after ur explaination now its clear

thanks a lot

Re: How to find the Units Digit
by Freaky Gadha - Sunday, 26 April 2009, 12:16 PM
  Hi Sibsankar,

How do u get the last two digits of 18^18 as 76???I got 24.
18^18 = (2* 3^2)^18=2^18 * (3^2)^18 = 2^10 *  2^8  * (3^4)^9=24 *  56  * 81^9=24*56*21=  24

therefore, 7^24  i.e., 7^4n = 1 (units digit) (answer)

regards,
fg

Re: How to find the Units Digit
by piyush ..............here - Wednesday, 29 April 2009, 10:45 PM
  @ sibsanakar.......

plzz tell us how can 2^even no. (in ques-- 7^18^18^18) will @ last become 0????
plz reply....
Re: How to find the Units Digit
by Sayan Majumder - Monday, 18 May 2009, 02:54 PM
  For this problem I don't think we need to do so much of calculations.

when you are taking any power of 18 (not 1 obviously) definitely it'll be a multiply of 4. (18=2*9, now when you are raising the power you'll get a multiply of 4)

So 7^4n will give you 1 as unit digit and in fact you can easily see last two digits will be 01. (7^4 gives 2401. 2401^n will give you last two digits as 01 always - you can take the reference from the chapter - "find out last two digits")


Please correct me if I am wrong...
Re: How to find the Units Digit
by chetan sinha - Tuesday, 19 May 2009, 07:38 PM
 

I CAN"T UNDERSTAND YOUR LAST EXAMPLE. PLEASE EXPLAIN IT. I AM NEW TO TG AND IT IS STUPENDOUS.

 

Re: How to find the Units Digit
by yogesh agarwal - Wednesday, 20 May 2009, 03:13 PM
 

I jus want to be clear wid one thing.. Will each and every number in the theorem ( i.e x ) will follow a cycle of 4??

 

Re: How to find the Units Digit
by Deepika Khandelwal - Thursday, 28 May 2009, 05:41 PM
  hi kamal...I am new in TG..
could you please explain how came 4k+(-1)odd from (8-1)odd

Re: How to find the Units Digit
by TG Team - Friday, 29 May 2009, 12:52 PM
  Hi Deepika smile

Using binomial theorem we get,
(a + b)n = ak + bn
as all terms of the expansion except the last term are multiple of a.

On the same lines
(8 - 1)odd = 8k + (-1)odd = 4m - 1
as 8k = 4(2k) = 4m and (-1)odd = -1.

Hope i am clear. smile
Re: How to find the Units Digit
by Priyesh Tungare - Thursday, 4 June 2009, 03:57 PM
  Hi,

In the question... find units digit of 4343-2222 , why the remainder of 4343 is 7 and 2222 is 4?
can someone explain me this?

i got 343 and 43/4 gives remainder of 3 and 222 gives remainder of  2.

so the diff remainder is 1.

Therefore the units digit of the ques shud be 1.

Please help me, where i am gng wrong....

Thanks,
Priyesh
Re: How to find the Units Digit
by dindo saha - Friday, 5 June 2009, 01:54 AM
  smile
hi priyesh,
(43)^43 unit digit equivalent to (3)^43s unit digit.
now (3)^43=(3^((4)*10)))*(3)^3.since (3)^4 has a power divisible by 4,3 odd so rem=1^10=1 unit (3)^3=7 .final unit (1*7)=7
(22)^22=(2^(4*5))*2^2 unit (2^4)=6(2 is even) 6^5=unit 6.
final unit =unit(6*4)=4
7-4=3 ans
Re: How to find the Units Digit
by dindo saha - Friday, 5 June 2009, 02:14 AM
  hi chetan,
7^(((11)^13)^17
consider the power 11^13^17.as per rule 11/4 rem =3 so 7^11 unit=7^3 unit=3
now rem table:
11^anything unit=1so 11^13^17=unit 1
thus final unit=3*1=3
Re: How to find the Units Digit
by discover legolas - Wednesday, 8 July 2009, 02:02 AM
  Hi Piyush,

for eg. x^n...the unit digit of this number depends upon the unit
digit of number 'x'. So for 43^43 can be written as 43^((4(10)+3)) therefore 3^3 which will give 7 as a unit digit. same for 22^22.
22^((4(5)+2)) therefore 2^2 which will give 4 as a unit digit.
Therefore
7-4=3.

P.S.
digit in the form x^(4n+1) will give the same digit x.
i.e. 3^5=**3.

Correct me if i'm wrong....


Regards
Legolas
Re: How to find the Units Digit
by sunakshi goel - Tuesday, 21 July 2009, 03:27 PM
  Thanks sir.Plz post me number system1:remainder
Re: How to find the Units Digit
by abhishek tripathi - Saturday, 22 August 2009, 01:03 AM
  nice one fundoo bro keep pondering more articles 4 da students of gadha .com cheers.
tg rockzzzzzzzzzzzsmile
Re: How to find the Units Digit
by robin madaan - Sunday, 13 September 2009, 06:43 AM
 

 her s a sum 4 evry1,,,lets see hw much u guys r done with ur basic unit digit

73249819367)^443^2153815365^27186872136876 +

32156127621373)^401^213767185613512356^2635162346512873315247147

+ 5^27315612365^1273483145371853

9^21671234615615276^5

= ????????????????

smile,,,,,,,,,tell me d answer,,,jst to confuse u so many terms

which r of no use,,,,lets test,,,tg u pz dnt reply,,,,lets us hav some fun here

right

love and light

robin

Re: How to find the Units Digit
by Netra Mehta - Sunday, 13 September 2009, 10:33 AM
  Hei Robin!
Is dere addition sign before 9^2167123415615276^5 ????

M givin my answer considering + sign there...
Q.
73249819367)^443^2153815365^27186872136876 +

32156127621373)^401^213767185613512356^2635162346512873315247147

+ 5^27315612365^1273483145371853 +

9^21671234615615276^5

Ans.
73249819367)^443^2153815365^27186872136876 Unit digit for this is - 3 since it is of the form (7)^4k+3

32156127621373)^401^213767185613512356^2635162346512873315247147
Its unit digit is - 3 since it is of the form (3)^4k+1

5^27315612365^1273483145371853 Unit digit is - 5 (since cyclicity for 5 is alwyz 1)

9^21671234615615276^5 Unit digit for this is - 1 since its of the form (9)4k


Adding all the unit digits we get the answer as...

3+3+5+1 = 12
n hence the unit digit for whole expression comes out to b - 2

Plz tell me the right answer Robin....
Correct me if m wrong sumwhr...






Re: How to find the Units Digit
by Netra Mehta - Sunday, 13 September 2009, 10:35 AM
  If in case dere is no + sign in the last term den dere r total 3 terms in the expression accordin to which the ans wud b...
3+3+5 = 11
Hence unit digit 1...
Re: How to find the Units Digit
by robin madaan - Monday, 14 September 2009, 10:12 PM
 

yes i 4get ther is a sign of + be4 9

73249819367)^443^2153815365^27186872136876 +

32156127621373)^401^213767185613512356^2635162346512873315247147

+ 5^27315612365^1273483145371853

+9^21671234615615276^5

and hey ny1 try dat sum

lets see who s right and who s nt

love and light

robin

Re: How to find the Units Digit
by robin madaan - Monday, 14 September 2009, 10:22 PM
 

yes u r rite

netra mehta,,,,

i dnt hav d answer bas dimaaaaaaag freeeeee mein khurapat kar raha tha,,,,,smilesmile

answer acc to me is also "2",,, and ther is a + sign be4 9

ciya

love and light

robinsmile

Re: How to find the Units Digit
by Priya Srivastava - Thursday, 17 September 2009, 01:19 PM
 

Hi Netra,

Can u plz explain me how to approach these kind of problems...i.e. x^y^z^a^b^c.....

how u calculated -- Unit digit for this is - 3 since it is of the form (7)^4k+3 & Its unit digit is - 3 since it is of the form (3)^4k+1.

Thanks

Priya

 

Logic Based Quant Question
by Pallav Jain - Thursday, 17 September 2009, 05:27 PM
 

Hi All,

Can anyone please explain me how to approach this kind of questions?

In a class of 30 students, there are 2 categories of students:
Liars: who always lie.
Truth Tellers: who always speak the truth.
These students make three different statements as follows :
Statement I :Seven of them say “ There are exactly 7 Liars in this class”
Statement II :Eight of them say “ There are exactly 8 Liars in this class”
Statement III :The rest of them say “ There are exactly 15 Liars in this class”.
How many Liars are there in the class ?

Options :-

a) 7      b) 8     c) 23     d) 22     e)  15    

Thanks,

Pallav

Re: How to find the Units Digit
by saurabh aggarwal - Thursday, 17 September 2009, 06:29 PM
  thank u sir for making me understand dis
topic wid such an ease!!!!!

SIR , i have problem in questions on "number of solutions of an equation" So , plz if u could help me in that area .....

Will wait for ur response.....b.t.w. thanks again smile
Re: How to find the Units Digit
by Netra Mehta - Friday, 18 September 2009, 03:01 AM
  Hi Priya!!
I reached thru d answer by cyclicity approach..

Evry no. hz a cyclicity..
for eg.
2,3,7,8 hv cyclicity of 4. this means after evry 4 powers the unit digit repeats for the no.
as in case...2^1=2 2^2=4 2^3=8 2^4=16 2^5=32 2^6=64 2^7=128 2^8=256
As u can see...the unit digits are repeatin after evry 4 nos. ie 2 4 8 6 den again 2 4 8 6

try this with powers of 3 7 & 8 also n u ll see dat in their case also cyclicity comes out to b 4

similarly cyclicity for 4 is 2.
for 1,5,6 cyc is 1 since for evry power unit digit for 5 ll remain alwyz 5 n similarly for 6 it ll remain 6...

so in all the cases try to put the nos. in form of 4k since e1 if cyclicity is 1 or 2 it is alwyz a factor of 4

so wen v write (7)^4k +3
its unit digit ll b same as (7)^3 ie 343 n hence 3
7 in (3)^4k + 1 it ll b same as 3^1 ie 3...

So in questions like x^y^x^a...
try to reduce y^x^a in the form of 4k + remainder...

I hope u got dat...
In case u still hv problem den go thru the concept of cyclicity n u ll understand it smile

Enjoy...
Re: Logic Based Quant Question
by Netra Mehta - Friday, 18 September 2009, 03:14 AM
  Hi Pallav!!!
Is d answer to ur question 15 ie option e ???
Do tell me the correct answer...

Netra
Re: Logic Based Quant Question
by Rahul Adwani - Friday, 18 September 2009, 11:30 AM
  e) 15
is it correct???
Re: How to find the Units Digit
by Janet W - Monday, 6 September 2010, 08:20 AM
  Thanks you for the post.

__________________
http://moviesonlineworld.com
Re: How to find the Units Digit
by Moksh Sharma - Friday, 10 September 2010, 12:36 AM
  Hello Netra..could you pls. help me understand, how did u get unit digit of 73249819367)^443^2153815365^27186872136876 as 1 ?

Thanks!

Moksh
Re: Logic Based Quant Question
by TG Team - Friday, 10 September 2010, 12:36 PM
 

Hi Pallav smile

It must be 15 only. smile

Re: Logic Based Quant Question
by mini gupta - Saturday, 11 September 2010, 06:55 PM
  HI Pallav,

Can u plese provide me the solution.. smile
Re: How to find the Units Digit
by Akshay Chaturvedi - Saturday, 11 September 2010, 09:19 PM
  Ya, 15 is correct : )

Kamal Sir, I have learned so much from you at the workshop. Looking forward to the next one ..
Re: How to find the Units Digit
by vijyeta rustagi - Wednesday, 6 April 2011, 06:20 PM
 

thanx a lot for explaining. this is the best explaination that helped me understand the concept once and for all.

Re: How to find the Units Digit
by nirlep singh - Wednesday, 1 June 2011, 10:13 PM
  sir here is 7^odd which means it may be 7^1 or 7^3 both give different results then how can we say that it would be 3.
Re: How to find the Units Digit
by TG Team - Thursday, 2 June 2011, 10:52 AM
 
Hi Nirlep smile

Kindly read the complete solution again. There I have found the remainder of power of 7 with 4 because unit digits repeat after every 4th power of the number. So I found that power of 7 there is of the form 4k - 1 = 4(k - 1) + 3 = 4k' + 3.

That means now I need to find the unit digit of 74k-1 = 74k'+3 = 73 = 3.

Don't hesitate for any further clarification , if required. smile

Kamal Lohia 
How to find the Units Digit
by Gayatri DHATRAK - Wednesday, 5 September 2012, 01:02 AM
  What is unit's digit of
(2^3^4^5^6) + (3^4^5^6^7)?

I got answer as a 3.. but i am not confirm
Re: How to find the Units Digit
by gaurav midha - Wednesday, 5 September 2012, 08:59 AM
  Gayatri,

Your answer is correct.
Re: How to find the Units Digit
by richa chhabra - Friday, 12 October 2012, 05:28 PM
  Can You please provide the solution for 8^10^12^14 unit digit by above method
Re: How to find the Units Digit
by Bugsy 123 - Friday, 12 October 2012, 08:35 PM
  Richa is from Infosys?
Re: How to find the Units Digit
by Bugsy 123 - Friday, 12 October 2012, 09:12 PM
  Can You please provide the solution for 8^10^12^14 unit digit by above method

Is the answer 6? :s
Re: How to find the Units Digit
by richa chhabra - Friday, 12 October 2012, 11:16 PM
 
and how did u get the ans?
yup.. from infy
Re: How to find the Units Digit
by Bugsy 123 - Saturday, 13 October 2012, 02:38 PM
  Can You please provide the solution for 8^10^12^14 unit digit by above method


I am not sure about this. But, considering the exponent, 10^12^14, it is of the form 4k. 8^4k would end in 6.
Re: How to find the Units Digit
by abhimanyu singh - Thursday, 25 October 2012, 08:15 PM
  hey richa..
8^10^12^14
in this question i think 8^10^(12*12*12.....14 time
as u can see 8 has more than two zero at last in power ...so it is divisible by 4
8^4k or (64*64)^k has 6 as its last digit
now..4096^k or 4096*4096 last digit still 6
6^k...as many times u multiply 6 by 6 it'll always end up as 6
Re: How to find the Units Digit
by sindhuja priyadarshini - Monday, 3 December 2012, 01:10 AM
  sir this article is really good
i wanted to know the solution for8^10^^12^14 smile
Re: How to find the Units Digit
by binu james - Thursday, 21 November 2013, 05:55 PM
 

A small doubt on case 1 and case 2 conditions:

Y or X which one we need to check whether it is odd or even ?

I think it is X.

Re: How to find the Units Digit
by TG team - Friday, 22 November 2013, 02:06 PM
  Hi binusmile

In case 2: When y is multiple of 4 , then we need to check whether x is even or odd.
If x is even-->(2,4,6,8) ,then xy will be 6
If x is odd -->(3,7,9) ,then xy will be 1.
Re: How to find the Units Digit
by Shivani K - Thursday, 26 November 2015, 03:16 PM
  Hi Gayatri,

Can u please elaborate on how did u get 3 as an answer to What is unit's digit of
(2^3^4^5^6) + (3^4^5^6^7)?
Re: How to find the Units Digit
by abhijeet dodiya - Sunday, 20 March 2016, 01:13 PM
  12^13^14^15
find unit digit of above expression