CAT 1999 | Question: 58

Question

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

• A. 0
• B. 1
• C. 49
• D. 341

Answer 1

$7^{84}=(7^{3})^{28}$

$\frac{ (7^{3})^{28} } {342}$ =$\frac{ (343 )^{28} } {342}$

Remainder of $\frac{ 343 } {342} =1$

As $7^{84}$ can be written as $(7^{3})^{28}$

The result will be $1^{28}$ =1

 

Hence Option (B)1 is the Answer.