divisibility math 2 to the power of 10 minus 1

[sree340]

210 - 1 is divisible by: 2 to the power of 10 minus 1

a. 31 b. 5 c. 7 d. 9 e. 13

any trick for getting solution

 

[soroban]

Hello, sree340!

\(\displaystyle 2^{10} - 1\,\text{ is divisible by: }\;(a)\;\;31\qquad(b)\;\;5\qquad(c)\;\;7\qquad(d)\;\;9\qquad(e)\;\;13\)

\(\displaystyle \text{Factor: }\;2^{10} - 1 \;=\;(2^5-1)(2^5+1) \;=\;(31)(33) \;=\;(31)(3)(11)\)