Quant: digital sum of 4444^4444

What is the digital sum of 4444^4444 ? Ans- 17

Solution:

Digital Sum implies that we keep on adding the digits of the result of 4444^4444 till we get a single digit number and that single digit number is the digital sum of the given number.

So, to find the digital sum of a given number, all we have to do is find the remainder when the number is divided by 9 and the remainder will be the required answer.

So, we find the remainder when 4444^4444 is divided by 9.

4444^4444 = (4446 - 2)^4444

Hence the remainder when 4444^4444 is divided by 9, is the same as the remainder obtained when 2^4444 is divided by 9.

2^4444 = {(2^3)^1481}*(2) = (8^1481)*(2) = {(9 - 1)^1481}*(2)

Hence the required remainder is: {(-1)^1481}*(2) = (-1)(2) = - 2 + 9 = 7

Thus, the digital sum of 4444^4444 is 7

Enjoy Maths.