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

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

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10 Aug 2006, 20:03
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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.
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10 Aug 2006, 20:45
jamesrwright3 wrote:
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.

E. it is not asking for how many different prime factors. actually the question is how many prime factors.

from i, m could be 3^n where n could be any finite integer or whole number.

from ii, m could be (3ab)^n where a and b could be any two different prime integers/numbers and n could be any finite integer or whole number.

from i and i, m is (9ab)^n where a and b could be any two different prime integers/numbers and any finite integer or whole number.

so it E...
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10 Aug 2006, 22:22
I have to agree with E.

1.) clearly insuff

2.) this could be more specific if it clarified only 2 prime numbers, but instead, there is an infinite number of possibilities.
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10 Aug 2006, 23:00
E.

1) m can be 3^x where x can be anything hence number of prime factor will keep on increasing with x

2) m = 3*P1*P2 where P1 and P2 are different prime numbers.
Hence m can be (3*P1*P2)^x. Not suff.

Together.

Also not Suff
10 Aug 2006, 23:00
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