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Different positive prime factors of positive integer n?

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Different positive prime factors of positive integer n?

by gmattesttaker2 » Mon Mar 31, 2014 9:43 pm
Hello,

For the following I had a very basic question. Is it correct that 1 is the prime factor of any other number? For instance, if n = 7 and the question asks how many different positive prime factors does the positive integer n have, would the answer be 2 in-this case i.e. the 2 numbers being 1 and 7?

Here is the question:

How many different positive prime factors does positive integer n have?

(1) Positive integer 2n is a multiple of 14.
(2) Positive integer n^2 has 3 different positive factors.

OA: B

Thanks a lot.

Best Regards,
Sri
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by Brent@GMATPrepNow » Mon Mar 31, 2014 9:46 pm
gmattesttaker2 wrote:Is it correct that 1 is the prime factor of any other number? For instance, if n = 7 and the question asks how many different positive prime factors does the positive integer n have, would the answer be 2 in-this case i.e. the 2 numbers being 1 and 7?
1 is not a prime number.
A prime number is a positive integer that has EXACTLY 2 factors.
So, for example, 3 is a prime number because its factors are 1 and 3
1, on the other hand, is not prime, because it has ONLY 1 factor (1)

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by [email protected] » Mon Mar 31, 2014 11:40 pm
Hi Sri,

This question is perfect for TESTing Values.

We're asked "how many different positive PRIME factors does N have?"

Fact 1: 2N is a multiple of 14

If N = 7, then then there is 1 prime factor (7)
If N = 14, then there are 2 prime factors (2 and 7)
Fact 1 is INSUFFICIENT

Fact 2: N^2 has 3 different positive factors

This is a rather restrictive piece of information, sine N^2 can only have 3 DIFFERENT factors.

If N = 2, N^2 = 4 (it's factors are 1, 2 and 4). N has 1 prime factor (2).
If N = 3, N^2 = 9 (it's factors are 1, 3 and 9). N has 1 prime factor (3).
N CANNOT be 4 because N^2=16 (and 16 has too many factors: 1, 2, 4, 8, 16)
If N = 5, N^2 = 25 (it's factors are 1, 5, 25). N has 1 prime factor (5)
Fact 2 is SUFFICIENT

Final Answer: B

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