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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8027
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the sum of the prime factors of 2^8-1?  [#permalink]

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22 Nov 2018, 02:22
1
1
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:14) correct 19% (01:09) wrong based on 53 sessions

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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Joined: 31 Oct 2013 Posts: 1465 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) What is the sum of the prime factors of 2^8-1? [#permalink] ### Show Tags 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. Intern Joined: 22 Nov 2018 Posts: 6 Re: What is the sum of the prime factors of 2^8-1? [#permalink] ### Show Tags 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 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] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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