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X, Y, and Z are three different prime numbers, the product XYZ

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Re: X, Y, and Z are three different prime numbers, the product XYZ

by Brent@GMATPrepNow » Sat Mar 07, 2020 5:40 am
BTGModeratorVI wrote: ↑
Fri Mar 06, 2020 5:51 pm
 X, Y, and Z are three different prime numbers, the product XYZ is divisible by how many different positive numbers?

A. 4
B. 6
C. 8
D. 9
E. 12

Answer: C
Source: GMATPrep
----ASIDE-------------------------
If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors.

Example: 14000 = (2^4)(5^3)(7^1)
So, the number of positive divisors of 14000 = (4+1)(3+1)(1+1) =(5)(4)(2) = 40
-----------------------------------
Since X, Y and Z are different PRIME numbers, we can say: XYZ = (X^1)(Y^1)(Z^1)
So, the number of positive divisors of XYZ = (1+1)(1+1)(1+1) =(2)(2)(2) = 8

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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