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Can 1 and the number itself be counted as divisors?

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by sleepingfool » Thu Nov 08, 2007 2:32 am
20. If n and p are different positive prime numbers, which of the integers , and np has (have) exactly 4 positive divisors?
(A) n4 only
(B) p3 only
(C) np only
(D) n4 and np
(E) p3 and np

Answer is E

but Does it count 1 or the number itself as divisor?
If yes, then E wrong because
p3 has 1 p p2 p3 and np has n p => total is 6 divisors
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Re: Can 1 and the number itself be counted as divisors?

by gabriel » Thu Nov 08, 2007 6:19 am
sleepingfool wrote:20. If n and p are different positive prime numbers, which of the integers , and np has (have) exactly 4 positive divisors?
(A) n4 only
(B) p3 only
(C) np only
(D) n4 and np
(E) p3 and np

Answer is E

but Does it count 1 or the number itself as divisor?
If yes, then E wrong because
p3 has 1 p p2 p3 and np has n p => total is 6 divisors
I dont think the question is asking for the total number of divisors, it is simply asking for the number of divisors of each integer .. hence the answer E ..

Also, the number it self and 1 are considered as divisors when u calculate the total number of divisors for any integer ...
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by showoff16884 » Sun Nov 11, 2007 7:45 pm
Gabriel is right. The question is asking for the the divisors for each integer

P3 > 1, P1, P2 & P3
NP > 1, N, P & NP

4 divisors for each integer. Answer choice E
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