Question

What is the remainder when 7^700 divided by 100 ?

Answer 1

Solution:

7^1 by 100 leaves a remainder of 7.

7^2 by 100 leaves a remainder of 49.

7^3 by 100 leaves a remainder of 43.

7^4 by 100 leaves a remainder of 1.

7^5 by 100 leaves a remainder of 7.

7^6 by 100 leaves a remainder of 49.
.....
.now…we have a repeating sequence with us, where the remainder is repeating for every 4 number’s…that’s 7^1 and 7^5 leaves the same remainder….

Coming to the answer…using this as the base 7^2 and 7^98 are the same.

hence 7^4 and 7^100 will have the same remainder as 1.

hence the solution to your answer is 1.