4^17-2^28??

Slim11 · Guest

The question asks: What is the greatest prime factor. The problem seems simple enough but it's disturbing when trying to solve quickly. Any hints

Guest · Posted: Fri Oct 12, 2007 1:07 am Post subject:

Answer would be 7.

4^17-2^28 = (2^2)^17 - 2^28 = 2^34 - 2^28 = 2^28 ( 2^6 - 1) = 2^28 * 63 = 2^28 * 9 * 7

This gives us 7 as a largest prime factor.

joshi.komal · Posted: Sun Oct 14, 2007 8:35 am Post subject:

The simplest approach to solving such questions is to try and come to a common base. Like write 4^28 in terms of the power of 2 which is the second term then you will have much clearer picture.

khurram · Posted: Mon May 26, 2008 3:22 pm Post subject:

finally after 30 minutes figured out how to make heads or tails.

frist make base same

2^34-2^28

divide both by 2^28.

equals 2^6-2^0

=64-1=63.

find lcm of 63 which is 7,3,1.

hence, 7 is the greatest prime factor.

Khurram