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What is the sum of the prime factors of 2^8-1?

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Math Revolution GMAT Instructor
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What is the sum of the prime factors of 2^8-1?  [#permalink]

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New post 22 Nov 2018, 02:22
1
1
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

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[Math Revolution GMAT math practice question]

What is the sum of the prime factors of \(2^8-1\)?

\(A. 8\)
\(B. 16\)
\(C. 19\)
\(D. 22\)
\(E. 25\)

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What is the sum of the prime factors of 2^8-1?  [#permalink]

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New post 22 Nov 2018, 02:26
MathRevolution wrote:
[Math Revolution GMAT math practice question]

What is the sum of the prime factors of \(2^8-1\)?

\(A. 8\)
\(B. 16\)
\(C. 19\)
\(D. 22\)
\(E. 25\)



\(2^8-1\)

\(2^{4*2}-1^2\)

\(( 2^4 + 1 ) ( 2^4 -1)\)

17 * 5 * 3

= 25

E is our answer.
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Re: What is the sum of the prime factors of 2^8-1?  [#permalink]

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New post 22 Nov 2018, 02:44
1
2^8= 2^4^2
1= 1^2
so the equation becomes
(2^4^2)-(1^2)
= (2^4-1)(2^4+1)
=(16-1)(16+1)
=15*17
=3*5*17

(3+5+17) = 25
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 8027
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: What is the sum of the prime factors of 2^8-1?  [#permalink]

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New post 25 Nov 2018, 18:36
=>

\(2^8-1 = (2^4+1)(2^4-1) = (2^4+1)(2^2+1)(2^2-1) = (2^4+1)(2^2+1)(2+1)(2-1) = 17*5*3*1.\)
Thus, the sum of prime factors of \(28-1\) is \(17 + 5 + 3 = 25.\)

Therefore, the answer is E.
Answer: E

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Re: What is the sum of the prime factors of 2^8-1?   [#permalink] 25 Nov 2018, 18:36
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