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If n is the product of 5 different prime numbers, how many f

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by Max@Math Revolution » Sun Jul 15, 2018 5:47 am

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[GMAT math practice question]

If n is the product of 5 different prime numbers, how many factors does n have?

A. 2
B. 4
C. 8
D. 16
E. 32
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by Max@Math Revolution » Sun Jul 15, 2018 5:05 pm
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Since p, q, r, s, t are different prime factors of n, we have n = p*q*r*s*t = p^1q^1r^1s^1t^1.
The number of factors of n is (1+1)(1+1)(1+1)(1+1)(1+1) = 2*2*2*2*2 = 32.

Therefore, the answer is E.
Answer: E
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by Scott@TargetTestPrep » Thu Jul 19, 2018 11:41 am
Max@Math Revolution wrote:[GMAT math practice question]

If n is the product of 5 different prime numbers, how many factors does n have?

A. 2
B. 4
C. 8
D. 16
E. 32
Using letters to represent the 5 different prime numbers, our product would be:

a^1 x b^1 x c^1 x d^1 x e^1

Recall that, to determine the total number of factors, we add 1 to each exponent and multiply, so we have:

(1 + 1)(1 + 1)(1 + 1)(1 + 1)(1 + 1) = 2^5 = 32

Answer: E

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