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


Human error. D'oh!
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 [#permalink] New post 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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