Problem Solving

BryanBTGMAT wrote:Can someone explain the ruled used on the bold line? I do not recall how this factoring works. Thank you!

4^17 - 2^28
Understood = (2²)^17 - 2^28
Understood = 2^34 - 2^28
Do not understand the factoring here= 2^28(2^6 - 1)
Understood = 2^28(63)
Understood = 2^28(7 * 3^2)

Therefore, the greatest prime factor of 4^17 - 2^28 is 7.

The correct answer is D.

2^34 - 2^28 = (2^28 * 2^6) - 2^28
Now, it can be seen that 2^28 is common in both the expressions above.
So, this can be simplified as 2^28(2^6 - 1) = 2^28(64 - 1) = 2^28(63)

I hope this helps.

BryanBTGMAT wrote:Can someone explain the ruled used on the bold line? I do not recall how this factoring works. Thank you!

4^17 - 2^28
Understood = (2²)^17 - 2^28
Understood = 2^34 - 2^28
Do not understand the factoring here= 2^28(2^6 - 1)
Understood = 2^28(63)
Understood = 2^28(7 * 3^2)

Therefore, the greatest prime factor of 4^17 - 2^28 is 7.

The correct answer is D.

HI BryanBTGMAT!

Anurag is exactly right that the 2 terms 2^34 and 2^28 both have a 2^28 in common, it just might help you to see it more explicitly...

We can re-write the terms...

2^34 = (2^28)(2^6) ...because if I were to multiply them I add the exponents...

2^28 = (2^28)(1) ...because any number times 1 is just that number...

Ok, so 2^34 - 2^28 = (2^28)(2^6) - (2^28)(1)

Since both terms have a 2^28, we can "factor" or pull that number outside of a new set of parenthesis and just leave the remainders inside...

2^28(2^6 - 1)

And from there you have the rest of your solution!

Hope this helps!

Whit