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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]  04 Jan 2007, 22:44
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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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1) m has two prime factore 3 and 3 â€¦ still we donâ€™t no the total number of prime factors.

Insufficient

2) m = 3^x * a ^y * b ^z â€¦ so we know that m has 3 different prime factors but still we donâ€™t know the total number of prime factors

Insufficeient

Senior Manager
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answer is C in my opinion....

st1: insuff, for example m=9 has only one prime factor. 18 has 2.
st2: insuff, for example m=18 (then m/3=6 has two prime factors) has 2 prime factors, and m=30 (m/3=10 has two prime factors) has 3 prime factors.

together they are sufficient:
st2 says that m/3 has 2 prime factors. so m/3=p^x*q^y where p and q are primes.
st1 claims that one of the two factors found in st2 is 3. or in other words
m/3=3^x*q^y (q is prime, x and y are integers)

from this we can infer: m = 3^(x+1)*q^y
so m has exactly 2 factors.

Last edited by hobbit on 05 Jan 2007, 07:50, edited 1 time in total.
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For me (C)

Stat 1
Brings nothing to conclude. We could have 2, 3 or 4.... prime factors.

INSUFF

Stat 2
o If m = 3*2*5 then m/3 = 2*5
o If m = 3*3*5 then m/3 = 3*5

We have the possibility to have 2 or 3 prime factors for m.

INSUFF

Both (1) and (2)
We are sure that m/3 has 3 like 1 prime factor and another prime factor only.

Thus,
m = 3^a*X^b where a is the power of 3, X is a prime number and b is the power of this prime number. Meanwhile, m has 2 prime factors.

SUFF.

Last edited by Fig on 05 Jan 2007, 08:05, edited 1 time in total.
Senior Manager
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of course C .... i gave an explanation for C just mistakenly wrote B.... (I edited it to eliminate any confusion....)
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I always get confused in these kinda problems? I cannot figure out whether the question is asking for all different prime factors or just all prime factors. I think the answer is C if the question is asking for all different prime factors, but E if its asking for all prime factors, including repeats.
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800_gal wrote:
I always get confused in these kinda problems? I cannot figure out whether the question is asking for all different prime factors or just all prime factors. I think the answer is C if the question is asking for all different prime factors, but E if its asking for all prime factors, including repeats.

in the set of all factors there are no repeats, and so is the set of prime factors.
so 4 has 3 factos 1,2,4 and only one prime factor (2)
it is true that 4 can be divided twice to 2... the decomposition of 4 to multiples of prime numbers has 2 twice.... but you must differentiate between decomposition of a number into primes and the prime factors of a number.... these are two different things.
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Thanks hobbit that really helps, I am taking the GMAT on Monday... Kinda freaking out at this point.
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Re: DS [ Prime Factor ] [#permalink]  05 Jan 2007, 14:14
johnycute 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.

(1) m/3 = multiple of 3 => m = 3 * mult of 3. m could be 3*3*1, 3*3*9824374978234, etc. Insuff => B, C or E.

(2) m/3 = p1 * p2 => m = 3 * p1 * p2. m could be 3*2*5, 3*3*5, 3*5*7, etc. Insuff => C or E.

(1&2) m = 3 * mult of 3 and m = 3 * p1 * p2 => m = 3 * 3 * prime => m has 2 prime factors: 3 and "prime".

C.
Re: DS [ Prime Factor ]   [#permalink] 05 Jan 2007, 14:14
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