Question

What is the remainder when ${25}^{36}$ is divided by 9?

• A. 5
• B. 1
• C. 3
• D. 7

Answer 1

The correct option is B 1

Again ${25}^{36}=(18+7{)}^{36}=(18+7\left)\right(18+7)...36$ times $=18K+7^{36}$
Hence remainder when ${25}^{36}$ is divided
by 9 is the remainder when $7^{36}$ is divided by 9.
Now $7^{36}=7^3\times 7^3\times 7^3...\left(12times\right)=343\times 343\times 343....\left(12times\right).$
When 343 is divided by 9, the remainder
is 1. Hence, the remainder when ${25}^{36}$ is divided by 9 is 1.