Which of the following is NOT a prime factor of

[BTGmoderatorDC]

Which of the following is NOT a prime factor of (5^6−2^6)?

A. 3
B. 7
C. 13
D. 17
E. 19


OA D

Source: Veritas Prep

[Scott@TargetTestPrep]

Which of the following is NOT a prime factor of (5^6−2^6)?

A. 3
B. 7
C. 13
D. 17
E. 19


OA D

Solution:

Factoring (5^6−2^6) as a difference of two squares, we have:

(5^3 + 2^3)(5^3 - 2^3) = (125 + 8)(125 - 8) = 133 x 117 = 7 x 19 x 9 x 13 = 3^2 x 7 x 13 x 19

We see that 17 is not a factor of 5^6 − 2^6.

Answer: D