Hi

For 7: make group of three digits together starting from unit digit side and make them alternate positive and negative with first group from unit digit side being positive. For example: 2123456789 = (-2 + 123 - 456 + 789) mod7 = 454 mod7 = 6 mod7.

For 37: make group of three digits together starting from unit digit side and all groups are positive. For example: 20103321 = (20 + 103 + 321) mod37 = 444 mod37 = 0 mod37.

Hope it is clear now.

Hi tgdel678 tg

First 32 is not a prime number, so you can't use the method you mentioned.

Now 32 = 2⁵ and recall that remainder when any number, N is divided by 2ⁿ is same as the remainder obtained by dividing number formed by last n-digits of N by same divisor 2ⁿ.

Hi Anila

It is 2ⁿ not 2n.

If you want to check whether N is divisible by 4 (2²) or not, just check the number formed by last 2 digits.

If you want to check whether N is divisible by 8 (2³) or not, just check the number formed by last 3 digits.

If you want to check whether N is divisible by 164 (2⁴) or not, just check the number formed by last 4 digits.

Similarly If you want to check whether N is divisible by 2ⁿ or not, just check the number formed by last n digits.

Hi tgdel678 tg,

Please tell the answer for the above question.

Hi  tgdel678 tg

just a quick way to find out remainder in this case, note that any number repeated 6 six times is always divisible by 3,7,11,13,37. As 259 has 7 and 37 as its prime factors, so by each of them remainder is 1, this is because the number 1 has been repeated 73 times , so the number 1 repeated 72 times will always be divisible by 7 and 37. hence by 259 remainder is 1. Also with 32 remainder will be 7, so R1 + R2 = 8