Question

What is the remainder if 8^25 is divided by 7?​

Answer 1

Step-by-step explanation:

The best way to find remainder is by using Fermat’s Little Theorem which suggests:

If p is a prime and a is any integer not divisible by p, then {a^(p − 1)}− 1 is divisible by p.

8 is not a prime number.

Let us check factors of 8 which are 1, 2, 4, 8. We found a prime number i.e. 2.

So 2^6 mod 7 = 1

Thus, we can say 2 raised to multiples of power 6 mod 7 will also give remainder as 1.

Also 8 = 2^3

Hence 8^25 = 2^75

Finally,

2^75 mod 7

= 2^{(6 x 12) + 3} mod 7

= [1] x 2^3 mod 7

= 8 mod 7

= 1

Your final answer is 1.

Answer 2

Answer:

8^(6*4)/7 = 1*4 = 1. 8^25/7 = 8^24/7 * 8/7 = 1 * 1 = 1.