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GRE Math Challenge #112-If n = pqr, where p, q, and r
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15 May 2015, 11:54
15 May 2015, 11:54
1
Expert Reply
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Question Stats:
53% (00:48) correct
46% (00:37) wrong based on 39 sessions
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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
(A) 3
(B) 5
(C) 6
(D) 7
(E) 8
Re: GRE Math Challenge #112
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27 Aug 2015, 18:31
27 Aug 2015, 18:31
1
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
Posted from my mobile device
p,q,r makes it another 3
n combinations of 2 from pqr - pq,qr,pr (gives it another 3)
So, answer is 8
Posted from my mobile device
Re: GRE Math Challenge #112-If n = pqr, where p, q, and r
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24 Jul 2020, 12:23
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
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
