Question

What will be the remainder when 7^100 is divided by 5?

Answer 1

Answer: 1

Step-by-step explanation:

Dividing the power of 2, i.e, 24 by 4 we get 0. That means the last digit of 2^24 will be same as last digit of 2^4 which is 6. Hence, when divided by 5 the remainder will be 1.

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Answer 2

Answer:

1

Step-by-step explanation:

This is a basic question of Chinese remainder theorem(CRT):

We can write 7^100 as (7^4)25.

Now, 7^4 = 2401 when we divide it by 5 then 1 will be the remainder.

Now, 7^100 as (7^4)^25 = (2401)^25 mod 5 = 1 ^25 mod 5 = 1.

Therefore, (7^100 % 5) = 1.