Question

What is remainder when $7^{84}$ is divided by 2402?

• A. 1
• B. 6
• C. 2401
• D. None of these

Answer 1

Answer: (C)

2401

$7^{84}$

$=(7^4{)}^{21}$

$=(2401{)}^{21}$

$=(2402-1{)}^{21}$

$=2402K+(-1{)}^{21}$

$=2402K-1$

Hence,the remainder when $7^{84}$ is divided by $2402$ is equal to $-1$ or $2402-1$

$=2401.$