Question

$4$ to the power $76+4$ to the power $77+4$ to the power $78+4$ to the power $79$ is divisible by ?

• A. $20$
• B. $68$
• C. Both A and B
• D. Neither A nor B

Answer 1

Answer: (C)

Both A and B

$4^{76}+4^{77}+4^{78}+4^{79}$
$=4^{76}(1+4+16+64)$
$=\left(4^{76}\right)\times 85$
It can be written as $4^{75}\times 4\times 5\times 17$
$=4^{74}\times 4\times 4\times 5\times 17$
$=4^{74}\times 20\times 68$
Thus, number is divisible by $68$ as well as $20$.