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GRE Math Challenge #112-If n = pqr, where p, q, and r

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sandy
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GRE Math Challenge #112-If n = pqr, where p, q, and r [#permalink] New post   15 May 2015, 11:54
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If n = pqr, where p, q, and r are three different positive prime numbers, how many different positive divisors does n have, including l and n?

(A) 3
(B) 5
(C) 6
(D) 7
(E) 8
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E
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Sakshi
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Re: GRE Math Challenge #112 [#permalink] New post   27 Aug 2015, 18:31
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1 and n makes it 2 divisors
p,q,r makes it another 3
n combinations of 2 from pqr - pq,qr,pr (gives it another 3)
So, answer is 8

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Re: GRE Math Challenge #112-If n = pqr, where p, q, and r [#permalink] New post   24 Jul 2020, 12:23
Another method of solving:

Total # of positive divisors of x^a * y^b * z^c, where x, y, and z are all prime is equal to (a+1) * (b+1) * (c+1)

So if n = p*q*r, and p, q, and r are all prime, then you can also write p*q*r as p^1 * q^1 * r^1.
Therefore, the total # of positive divisors of n = (1+1) * (1+1) * (1+1) = 8

E is the answer
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Re: GRE Math Challenge #112-If n = pqr, where p, q, and r [#permalink] New post   29 Jul 2020, 06:13
sandy wrote:
If n = pqr, where p, q, and r are three different positive prime numbers, how many different positive divisors does n have, including l and n?

(A) 3
(B) 5
(C) 6
(D) 7
(E) 8


Another approach is to test some values that satisfy the given conditions

n = pqr, where p, q, and r are three different positive prime numbers
Let p = 2
Let q = 3
Let r = 5

So, n = pqr = (2)(3)(5) = 30


How many different positive divisors does n have, including 1 and n?
In other words, "How many different positive divisors does 30 have, including 1 and 30?"

The positive divisors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30
There are 8 positive divisors

Answer: E

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Brent
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Re: GRE Math Challenge #112-If n = pqr, where p, q, and r [#permalink]
29 Jul 2020, 06:13
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