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Prime factors.

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by lenagmat » Tue Oct 25, 2011 9:42 am
Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

A). 4
B). 5
C). 6
D). 7
E). 8
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by Anurag@Gurome » Tue Oct 25, 2011 10:05 am
lenagmat wrote:Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?
As the GCF of m and n is 15 = 3*5, m and n both must have 3 and 5 as their prime factors. Hence, the other two prime factors of m and the third prime factor n must be different from each other.

Hence, the different prime factors of mn are 3, 5, two other prime factors of m and third prime factor of n.

Hence, number of different prime factors of mn = 2 + 2 + 1 = 5

The correct answer is B.
Last edited by Anurag@Gurome on Tue Oct 25, 2011 9:45 pm, edited 1 time in total.
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by samyukta » Tue Oct 25, 2011 11:54 am
IMO B ) 5

since m has 4 out of which 2 goes to 15 ( 5,3)
n has 3 out of which 2 goes 15 ( 5,3)

so we have 3, 5,m1 ,m2, n1 = 5 different prime numbers.
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by rooster » Tue Oct 25, 2011 6:50 pm
Anurag@Gurome wrote:
lenagmat wrote:Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?
As the GCF of m and n is 15 = 3*5, m and n both must have 3 and 5 as their prime factors. Hence, the other two prime factors of both m and n must be different from each other.

Hence, the different prime factors of mn are 3, 5, two other prime factors of m and two other prime factors of n.

Hence, number of different prime factors of mn = 2 + 2 + 2 = 6

The correct answer is C.
It says m has 4 different prime factors and n has 3

Thus that should mean the two prime factors shared from m&n and then the separate factors from m=2 and n=1, which comes out to 5, [spoiler]so the answer should be B(5)[/spoiler]
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by Brent@GMATPrepNow » Tue Oct 25, 2011 9:16 pm
lenagmat wrote:Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

A). 4
B). 5
C). 6
D). 7
E). 8
Alternatively, we could pick some numbers that satisfy the given conditions.
As was already pointed out, we know that m and n must share a 3 and a 5 in their prime factorizations.
So, one possibility is: m=2x3x5x7 and n=3x5x11

This means that mn = 2x2x3x5x5x7x11
Here we can see that mn has 5 different prime factors. They are 2, 3, 5, 7, and 11

So, the answer is B

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by Anurag@Gurome » Tue Oct 25, 2011 9:45 pm
Made a silly mistake.
Edited the reply.
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by parul9 » Thu Oct 27, 2011 9:55 am
m = 3 * 5 * p1 * p2
n = 3 * 5 * p3

mn = 3^2 * 5^2 * p1 * p2 * p3

Prime factors of mn = 3, 5, p1, p2, p3
5 in all.

So, B is the answer.
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hi

by Jeff@TargetTestPrep » Wed Dec 13, 2017 10:22 am
lenagmat wrote:Integer m has 4 different prime factors and n has 3 different prime factors. If m and n has the greatest common factor of 15, how many different prime factors does mn have?

A). 4
B). 5
C). 6
D). 7
E). 8
If m and n have a GCF of 15, they both share a prime of 3 and 5. Thus, m has 2 prime factors that differ from those of n and n has 1 other prime factor that differs from those of m.

Since mn has 2 common prime factors and 3 uncommon prime factors, mn has a total of 5 different prime factors.

Answer: B

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