Can someone help with this question from the free software?

[simunda]

Hope I'm not breaking any rules here but I have come across this question a couple of times on the free official software CATs and just cannot work out how the answer is reached. Can anyone help?

What is the greatest prime factor of 4 to power 17 minus two to power 28?

Thanks.....

[Bharat]

Answer: 7

4^17 - 2^28
= 2^34 - 2^28
= 2^28 ( 2^6 - 1)
= 2^28 (64-1)
= 2^28 (7*9)
= 2^28 * 3^2 * 7 --> 7 is the largest prime here.

Regards.

[simunda]

Thanks , that helps a lot. I kept getting the first few steps but got the difference to be 2^6.....could you explain why its 2^6-1 please?

[Bharat]

Answer: 7

4^17 - 2^28
= 2^34 - 2^28
= 2^28 ( 2^6 - 1)
= 2^28 (64-1)
= 2^28 (7*9)
= 2^28 * 3^2 * 7 --> 7 is the largest prime here.

Regards.

2^34 = 2^28 * 2^6 [exponents of the same base are added during multiplication]
revisit the 2nd line of the answer again:
2^34 - 2^28
= 2^28 * 2^6 - 2^28 * 1
=2^28 (2^6 - 1) [2^28 is common]
Let me know if this does not help.

[simunda]

perfect, thank you so much, got it now!

[zachthegnome]

I am still missing something on the 2^6-1 step.

Please elaborate further. Thanks.

[Bharat]

I am still missing something on the 2^6-1 step.

Please elaborate further. Thanks.

I have used the following two formulas:
1. a = a*1
2. a*b - a*1 = a (b - 1)

In these, replace "a" with "2^28" & "b" with "2^6"; & you will get the requisite step.

Let me know if there are any ambiguities. Thanks.