GREATEST PRIME FACTOR

[Mclaughlin]

What is the greatest prime factor of 4^14-2^28?

2
3
5
7
11

[ramyaravindran]

Is the question correct?. From how I read the question when you simplify the equation it comes out to be zero. 4^14 - 2^28 => 2^28 -2^28 => 0.

[Mclaughlin]

oh shoot i'm sorry, i typed it wrong. heres the right question...

What is the greatest prime factor of 4^17-2^28?

2
3
5
7
11

[ramyaravindran]

You can simplify the above equation as follows

4^17 - 2 ^ 28

(2^2)^17 - 2 ^ 28

2^34 - 2^28

this can be written as

2^28(2^6 - 1)

2^28(64-1)

2^28 * 63 => 2^28*7*3*3

The greatest prime number for the above would be 7. So the answer should be D.

[pepeprepa]

The same: 7

[uncbeers]

You can simplify the above equation as follows

4^17 - 2 ^ 28

(2^2)^17 - 2 ^ 28

2^34 - 2^28

this can be written as

2^28(2^6 - 1)

2^28(64-1)

2^28 * 63 => 2^28*7*3*3

The greatest prime number for the above would be 7. So the answer should be D.

For some reason I am missing how you went from step 3 to step 4 here. How does 2^34 - 2^28 become 2^28(2^6 - 1)?

Thank you!

[pepeprepa]

For some reason I am missing how you went from step 3 to step 4 here. How does 2^34 - 2^28 become 2^28(2^6 - 1)?

Thank you!

2^34=2^28 * 2^6
a^(b+c)= a^b * a^c
So we have
A= 2^34 - 2^28
A= 2^28 * 2^6 - 2^28
A= 2^28 ( 2^6 -1)

[uncbeers]

Should've guessed...lol. Thanks-makes perfect sense now!

[sanju09]

4^17 = (2^2)^17 = 2^34

2^34 - 2^28 = 2^28*(2^6 - 1) = 2^28*63 = 2^28 * 7 * 3^2

so 7

[anthony.j]

Ahhh.... I finally figured it out after writing it down on paper. You turned 2^34 into two number 2^6 and 2^28. Now the two 2^28 cancel each out out leaving 2^1 * 2^6

The rest is just simplifying.

Thanks!