prime integers

What is the greatest prime factor of 6� − 3�?

a) 3
b) 11
c) 17
d) 19
e) 31

6� − 3� is a DIFFERENCE OF SQUARES. So we can factor it.
6� − 3� = (6� + 3�)(6� - 3�)
= (6� + 3�)(6² + 3²)(6² - 3²)
= (6� + 3�)(6² + 3²)(6 + 3)(6 - 3)
= (6� + 3�)(45)(9)(3)
= (6� + 3�)(3)(3)(5)(3)(3)(3)

Hmmmm, we can see that the correct answer is "hiding" in the first number (6� + 3�)
Let's factor out the 3�, to get:
6� + 3� = 3�(2� + 1)
= 3�(16 + 1)
= 3�(17)
= (3)(3)(3)(3)(17)

So, 6� − 3� = (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

What is the greatest prime factor of 6� − 3�?

a) 3
b) 11
c) 17
d) 19
e) 31

Another approach:

6� − 3� = 3�(2� − 1)
= 3�(2� + 1)(2� − 1)
= 3�(16 + 1)(16 − 1)
= 3�(17)(15)
= 3�(17)(3)(5)

Aha - 17 is the greatest prime factor

Answer: C

Cheers,
Brent