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# If n is the product of 3 different prime numbers, how many factors doe

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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If n is the product of 3 different prime numbers, how many factors doe  [#permalink]

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02 Oct 2017, 01:57
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Difficulty:

25% (medium)

Question Stats:

75% (01:06) correct 25% (01:03) wrong based on 88 sessions

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[GMAT math practice question]

If n is the product of 3 different prime numbers, how many factors does n have except 1 and n?

A. 6
B. 7
C. 8
D. 9
E. 10

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 3138 Location: India GPA: 3.12 If n is the product of 3 different prime numbers, how many factors doe [#permalink] ### Show Tags 02 Oct 2017, 02:09 MathRevolution wrote: [GMAT math practice question] If n is the product of 3 different prime numbers, how many factors does n have except 1 and n? A. 6 B. 7 C. 8 D. 9 E. 10 Let the 3 different prime numbers be a,b,and c. If $$n = a^x*b^y*c^z$$ where x,y, and z are the powers of the respective prime numbers then the number "n" has $$(x+1)(y+1)(z+1)$$ factors. In this case, x=y=z=1, the number n will have 2*2*2 or 8 factors. Therefore, excluding 1 and n, the number n has 6 factors(Option A) _________________ You've got what it takes, but it will take everything you've got Intern Joined: 02 Sep 2017 Posts: 3 Re: If n is the product of 3 different prime numbers, how many factors doe [#permalink] ### Show Tags 03 Oct 2017, 14:40 1 Or try plugging in numbers: We need 3 different prime numbers, so try {2,3,5} 2*3*5=30 Find the factors of 30 other than 1 and 30 3*10 (that's two) 2*15 (four) 6*5 (six) Answer is A Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6239 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If n is the product of 3 different prime numbers, how many factors doe [#permalink] ### Show Tags 04 Oct 2017, 01:43 => n = p*q*r where p, q and r are different prime numbers. Then the number of factors of n is (1+1)(1+1)(1+1) = 8 including 1 and n, since the exponents of p, q and r are 1. Thus the number of factors of n except 1 and n is 8 – 2 = 6. Answer: A _________________ 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$99 for 3 month Online Course"
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Re: If n is the product of 3 different prime numbers, how many factors doe &nbs [#permalink] 04 Oct 2017, 01:43
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# If n is the product of 3 different prime numbers, how many factors doe

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