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greatest prime factor of the product nt?

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by jain2016 » Wed May 04, 2016 10:21 pm
If n and t are positive integers, what is the greatest prime factor of the product nt?

1) The greatest common factor of n and t is 5

2) The least common multiple of n and t is 105.

OAB

Hi Experts ,

Please explain.

Many thanks in advance.

SJ
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by Brent@GMATPrepNow » Thu May 05, 2016 9:34 am
There are some solutions here: https://www.beatthegmat.com/lcm-gcd-t276297.html

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by [email protected] » Thu May 05, 2016 9:43 am
Hi jain2016,

This DS prompt is based on some Number Properties and is perfect for TESTing VALUES.

We're told that N and T are positive integers. We're asked for the greatest PRIME factor of NT.

Fact 1: The Greatest Common Factor of N and T is 5

For the GCF to be 5, that means that BOTH N and T have to be multiples of 5

If N=5, T=5, then NT = 25 and the answer to the question is 5
If N=5, T=35, then NT = 175 and the answer to the question is 7
Fact 1 is INSUFFICIENT

Fact 2: The Least Common Multiple of N and T is 105

For the LCM to be 105, that means that BOTH N and T have to be ODD (since even numbers can never have an odd LCM) and at least one MUST be a multiple of 5.

Also, since both numbers MUST be ODD, the LCM IS the product of NT.

105 = (3)(5)(7), so no matter how you choose your N and T:

1 and 105
3 and 35
5 and 21
7 and 15

The answer to the question will ALWAYS be 7.
Fact 2 is SUFFICIENT

Final Answer: B

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by Mo2men » Sun Aug 20, 2017 1:36 am
[email protected] wrote:Hi jain2016,

This DS prompt is based on some Number Properties and is perfect for TESTing VALUES.

We're told that N and T are positive integers. We're asked for the greatest PRIME factor of NT.

Fact 1: The Greatest Common Factor of N and T is 5

For the GCF to be 5, that means that BOTH N and T have to be multiples of 5

If N=5, T=5, then NT = 25 and the answer to the question is 5
If N=5, T=35, then NT = 175 and the answer to the question is 7
Fact 1 is INSUFFICIENT
Dear Rich,

In Statement 1:

If n = 5 & t =45....then GCF =5 but what is the greatest prime factor of 'nt' ?? Is it 3^2 or 5?? When used term 'greatest prime' factor, should we include power or ignore it?

Thanks
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by DavidG@VeritasPrep » Sun Aug 20, 2017 3:28 am
Mo2men wrote:
[email protected] wrote:Hi jain2016,

This DS prompt is based on some Number Properties and is perfect for TESTing VALUES.

We're told that N and T are positive integers. We're asked for the greatest PRIME factor of NT.

Fact 1: The Greatest Common Factor of N and T is 5

For the GCF to be 5, that means that BOTH N and T have to be multiples of 5

If N=5, T=5, then NT = 25 and the answer to the question is 5
If N=5, T=35, then NT = 175 and the answer to the question is 7
Fact 1 is INSUFFICIENT
Dear Rich,

In Statement 1:

If n = 5 & t =45....then GCF =5 but what is the greatest prime factor of 'nt' ?? Is it 3^2 or 5?? When used term 'greatest prime' factor, should we include power or ignore it?

Thanks
Always take the prompt literally. 3^2 = 9, which isn't prime. In other words, because an exponent > 1 would make the factor non-prime, you'd ignore it.
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by Mo2men » Tue Aug 22, 2017 12:17 pm
DavidG@VeritasPrep wrote:
Always take the prompt literally. 3^2 = 9, which isn't prime. In other words, because an exponent > 1 would make the factor non-prime, you'd ignore it.
Dear David,

Thanks for your reply.

I might find my confusion but I need your support.

Is the meaning different in case the stem says 'greatest prime number' instead of 'greatest prime factors'

My understanding is that, for example' 12 = 2 ^2 * 3. We say that 2 & 3 are prime factors of 12. We do not ignore 2 as prime number just because it is raised to power 2.

Thanks in advance
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by [email protected] » Tue Aug 22, 2017 1:37 pm
Hi Mo2men,

The term 'greatest prime factor' means "the biggest prime that divides evenly into a number"

For example, 45 has two different prime factors: 3 and 5... Thus, the greatest prime factor is 5.

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by DavidG@VeritasPrep » Tue Aug 22, 2017 4:10 pm
Mo2men wrote:
DavidG@VeritasPrep wrote:
Always take the prompt literally. 3^2 = 9, which isn't prime. In other words, because an exponent > 1 would make the factor non-prime, you'd ignore it.
Dear David,

Thanks for your reply.

I might find my confusion but I need your support.

Is the meaning different in case the stem says 'greatest prime number' instead of 'greatest prime factors'

My understanding is that, for example' 12 = 2 ^2 * 3. We say that 2 & 3 are prime factors of 12. We do not ignore 2 as prime number just because it is raised to power 2.

Thanks in advance
Well, I'm not sure if there's any reasonable way to reword the stem without using a term such as "factor" or "divisor" but it might be helpful to think about it like this:

Take your analysis of 12. We could look at the prime factorization, 2^2 * 3, in which case the prime bases - and therefore the prime factors - are 2 and 3. (And note that the remaining factors can be assembled using those bases. 4 = 2^2; 6 = 2*3, etc.) Or we could look at the list of all the factors of 12: 1, 2, 3, 4, 6, 12, and see that the only prime factors are 2 and 3. Either method would be a reasonable way to arrive at the conclusion that 12 has two prime factors and that the largest prime factor is 3.
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