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If n = 4p, where p is a prime number greater than 2, how man

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Carcass
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If n = 4p, where p is a prime number greater than 2, how man [#permalink] New post   07 Aug 2020, 10:00
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If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight


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C
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chacinluis
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Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink] New post   09 Aug 2020, 09:44
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n=4p
Since p is a prime number greater than 2, then p is odd.
Also since p is prime the only factors of p are p and 1.

factors of 4p are: 1,2,4,p,2p,4p
Therefore
2,4,2p,4p are all even factors
The fact that p is not 2 and not 1, tells us 2p is not 4 and 4p is not 1 correspondingly. So they are all distinct.

Final Answer: 4
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Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink] New post   07 Aug 2020, 10:42
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Carcass wrote:
If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight


Kudos for the right solution and explanation


We can solve a lot of Integer Properties questions by testing a value

If p is prime, let's let p = 3
So, n = 4p = (4)(3) = 12

The positive EVEN divisors of 12 are: 2, 4, 6 and 12
So, there are FOUR even divisors of n.

Answer: C

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If n = 4p, where p is a prime number greater than 2, how man [#permalink] New post   07 Sep 2022, 20:12
chacinluis wrote:
n=4p
Since p is a prime number greater than 2, then p is odd.
Also since p is prime the only factors of p are p and 1.

factors of 4p are: 1,2,4,p,2p,4p
Therefore
2,4,2p,4p are all even factors
The fact that p is not 2 and not 1, tells us 2p is not 4 and 4p is not 1 correspondingly. So they are all distinct.

Final Answer: 4


Can someone explain the reason behind the highlighted portion above?
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Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink] New post   07 Sep 2022, 23:25
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I suggest you to read our Quant book: the section how to find the factor of a number.

Finding the Number of Factors of an Integer

https://gre.myprepclub.com/forum/gre-quant ... tml#p51913

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Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink] New post   20 Jun 2023, 13:32
n=4p, where p is some prime greater than 2 (p=3,5,7,11,13...)
Lets just assume that p=5. We know from number properties, that because p will not be raised to any power or such, the answer will not change if p is 5 or 17 or 11 etc.
n=20=2*2*5
n has a total of (2+1)(1+1)=6 factors
Of these factors the only odds one are: 1 and 5
the rest must be even divisors. So it has 2 odd divisors and 4 even divisors.

C
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Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink] New post   13 Sep 2024, 22:46
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Re: If n = 4p, where p is a prime number greater than 2, how man [#permalink]
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