Question

$(2^{51}+2^{52}+2^{53}+2^{54}+2^{55})$ is divisible by

• A. $23$
• B. $58$
• C. $124$
• D. $127$

Answer 1

Answer: (C)

$124$

$2^{51}+2^{52}+2^{53}+2^{54}+2^{55}$

$=2^{51}[1+2+2^2+2^3+2^4]=2^{51}[1+2+4+8+16]$

$=2^{51}\times 31=2^{49}\times 124$

Hence, the expression is divisible by $124$.