Question

Consider the number $N=2^{24}-1$.
Number of two digit divisors of $N$, is

• A. 14
• B. 12
• C. 10
• D. 8

Answer 1

Answer: (B)

$2^{24}-1=\left(2^{12}+1\right)\left(2^{12}-1\right)=\left(2^{12}+1\right)\left(2^6+1\right)\left(2^6-1\right)$
$=4097\cdot 65\cdot 63=241\cdot 17\cdot 5\cdot 13\cdot 7\cdot 3^2$
Number of two digit divisior $13;17;21;39;15;51;63;45;91;35;65;85\to 12$ divisors.