If m is divisible by 3, how many prime factors does m have?

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If m is divisible by 3, how many prime factors does m have? [#permalink]

22 Jun 2010, 00:12

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If m is divisible by 3, how many prime factors does m have?
1). m/3 is divisible by 3.
2). m/3 has two different prime factors.

I've seen answers given as

[Reveal] Spoiler:

B , C and E

by different people.
I would go for E
1. if m has 3 and m/3 has a 3, then m has at least 3^2, but m may have other factors..
2.m has a 3 and 2 different primes (x,y) from m/3. So m has at least 3,x,y if not more. But either x or y could be a 3 as well. in that case m has 3^2,x or 3^2,y
1+2
m/3 has a 3 and another prime factor x
m then has 3^2, x, and other factors that we dont know about

According to mgmat book, since m is a variable, we couldn't tell how many prime factors if we don't have constraint m
Could someone post the correct solution?

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Re: Prime factor:Can someone give a definite answer? [#permalink]

22 Jun 2010, 03:06

Pipp wrote:

According to mgmat book, since m is a variable, we couldn't tell how many prime factors if we don't have constraint m

what does this mean ?

:?:

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Last edited by intellijat on 22 Jun 2010, 05:51, edited 1 time in total.

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Re: Prime factor:Can someone give a definite answer? [#permalink]

22 Jun 2010, 03:11

m is divisible by 3. How many prime factors does m have?

1. Remember, we also consider zero to be perfectly divisible by any number, and hence m could be some multiple of 3 greater than 3, or zero. INSUFF

2. m/3 has 2 prime factors. say x and y. So m = 3 * x^k * y^n
If m = 2*3*5, then m/3 = 2*5. So m has 3 prime factors
If m = 3^2 * 5 then m/3 = 3*5, but m has only 2 prime factors, insufficient.

Both 1 and 2.

Since m/3 is divisible by 3, one of the prime factors of m/3 is 3
So m/3 = 3^n * y^k => m = 3^(n+1) * y^k
Thus m also has 2 prime factors.

Pick C.

Remember we are only concerned with prime factors, which are counted only once each irrespective of how many times they occur in the prime factorization of a number.

Re: Prime factor:Can someone give a definite answer? [#permalink] 22 Jun 2010, 03:11

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If m is divisible by 3, how many prime factors does m have?

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If m is divisible by 3, how many prime factors does m have?

If m is divisible by 3, how many prime factors does m have?

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