Question

The remainder when $7^{84}$ is divided by 342 is

• A. 1
• B. 49
• C. 341

Answer 1

The correct option is A 1

$7^3=343$, when divided by 342, leaves a remainder of 1
$7^4=2401$, when divided by 342, leaves a remainder of 7
$7^5=16807$, when divided by 342, leaves a remainder of 49
$7^6=117649$, when divided by 342, leaves a remainder of 1
And so on
$\therefore 7^{84}$, when divided by 342, will leave a remainder of 1