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If N = 6p, where p is a prime number greater than 3, how many differen

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Bunuel
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If N = 6p, where p is a prime number greater than 3, how many differen [#permalink] New post   07 Dec 2020, 02:45
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If N = 6p, where p is a prime number greater than 3, how many different positive even divisors does N have, including N itself?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
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C
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gornexq
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If N = 6p, where p is a prime number greater than 3, how many differen [#permalink] New post   Updated on: 07 Dec 2020, 03:23
C. Yup right! Since the even postivie divisors would be 2,6, 2p and N.

Posted from my mobile device

Originally posted by gornexq on 07 Dec 2020, 02:55.
Last edited by gornexq on 07 Dec 2020, 03:23, edited 3 times in total.
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If N = 6p, where p is a prime number greater than 3, how many differen [#permalink] New post   07 Dec 2020, 03:11
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gornexq wrote:
B. Since the even postivie divisors would be 2,6 and N.

Posted from my mobile device

Hi,
You are missing another even factor 2p.

Let us solve this elaborately.

Given N = 6p = 2*3*p
Total number of factors is (a+1)*(b+1)*(c+1) for 2^a*3^b*p^c.

In this case it is (1+1)*(1+1)*(1+1) which is 8

Number of odd factors can be calculated as factors of 3 and p which is (1+1)*(1+1) which is 4.

Total number of even factors = total number of factors - total number of odd factors
= 8-4
= 4

Ans C

Hope this clarifies.
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Re: If N = 6p, where p is a prime number greater than 3, how many differen [#permalink] New post   07 Dec 2020, 07:39
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Bunuel wrote:
If N = 6p, where p is a prime number greater than 3, how many different positive even divisors does N have, including N itself?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 8


N = 6p, where p is a prime number greater than 3
So, it COULD be the case that p = 5, which means N = 6p =6(5) = 30

How many different positive even divisors does N have, including N itself?
The positive divisors of 30 are: 1, 2, 3, 5, 6, 10, 15 and 30
The EVEN divisors are 2, 6, 10 and 30

Answer: C
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Re: If N = 6p, where p is a prime number greater than 3, how many differen [#permalink] New post   07 Dec 2020, 10:23
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Asked: If N = 6p, where p is a prime number greater than 3, how many different positive even divisors does N have, including N itself?

N = 2*3*p
Since p is odd
Even divisors of N = {2, 6, 2p, 6p}

IMO C
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Re: If N = 6p, where p is a prime number greater than 3, how many differen [#permalink] New post   02 Dec 2022, 03:42
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Re: If N = 6p, where p is a prime number greater than 3, how many differen [#permalink]
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