BTGModeratorVI wrote: ↑Mon Jun 22, 2020 6:11 am
What is the greatest prime factor of 6^8 − 3^8 ?
A) 3
B) 11
C) 17
D) 19
E) 31
Answer:
C
Source: Veritas Prep
6^8 − 3^8 is a DIFFERENCE OF SQUARES. So we can factor it.
6^8 − 3^8 = (6^4 + 3^4)(6^4 - 3^4)
= (6^4 + 3^4)(6^2 + 3^2)(6^2 - 3^2)
= (6^4 + 3^4)(6^2 + 3^2)(6 + 3)(6 - 3)
= (6^4 + 3^4)(45)(9)(3)
= (
6^4 + 3^4)(3)(3)(5)(3)(3)(3)
Hmmmm, we can see that the correct answer is "hiding" in the first number (
6^4 + 3^4)
Let's factor out the 3^4, to get:
6^4 + 3^4 = 3^4(2^4 + 1)
= 3^4(16 + 1)
= 3^4(17)
= (3)(3)(3)(3)(17)
So, 6^8 − 3^8 =
(3)(3)(3)(3)(17)(3)(3)(5)(3)(3)(3)
So the correct answer is C
ASIDE: For more on factoring differences of squares, see our free video -
https://www.gmatprepnow.com/module/gmat- ... /video/955
Cheers,
Brent
