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If n = 4p, where p is a prime number greater than 2, how man
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07 Aug 2020, 10:00
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
Kudos for the right solution and explanation
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Kudos for the right solution and explanation
Re: If n = 4p, where p is a prime number greater than 2, how man
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09 Aug 2020, 09:44
09 Aug 2020, 09:44
10
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
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
General Discussion
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Re: If n = 4p, where p is a prime number greater than 2, how man
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07 Aug 2020, 10:42
07 Aug 2020, 10:42
5
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
(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
Cheers,
Brent
