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# From OG, How many different positive intergers are factors

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Manager
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From OG, How many different positive intergers are factors [#permalink]  31 Jan 2004, 17:48
From OG,
How many different positive intergers are factors of 441?

This question is, per se, easy. But, who can demonstrate the most elegant approach, other than traditional method, to solve it?
Director
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[#permalink]  02 Feb 2004, 07:27
Wouldn't the most elegant approach be a simple factorization?
441=
3*3*7*7

1, 3, 9, 21, 63, 147, 441
SVP
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[#permalink]  02 Feb 2004, 08:46
Hi stoolfi,

You mean factorization into primes.

3^2 * 7^2

3^1, 3^2, 3*7^1, 3*7^2, 3^2*7^1, 3^2*7^2
7, 7^2

7 factors.
Senior Manager
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[#permalink]  02 Feb 2004, 09:45
stoolfi wrote:
Wouldn't the most elegant approach be a simple factorization?
441=
3*3*7*7

1, 3, 9, 21, 63, 147, 441

Stoolfi,

Why you omitted 7 and 49? Total should 9 factors
SVP
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[#permalink]  02 Feb 2004, 10:41
yeah there should be 9 factors. I did not include 1
Director
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[#permalink]  02 Feb 2004, 10:56
Quote:
Why you omitted 7 and 49? Total should 9 factors.

Human error. D'oh!
Manager
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[#permalink]  02 Feb 2004, 18:01
Thanx a lot,
I just learn from other comparable topic in this GMAT webboard that this genre of question we can apply:
441 = (3^2)*(7^2)

thus, we have 9 factors; that are {1,3,9}*{1,7,49) = 9 patterns

Well, try another OG quiz,

If n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
[#permalink] 02 Feb 2004, 18:01
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# From OG, How many different positive intergers are factors

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