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What is the quickest way to calculate factors of a given

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What is the quickest way to calculate factors of a given [#permalink] New post 29 Aug 2007, 18:03
What is the quickest way to calculate factors of a given integer?

Eg.. how many factors does 441 have?
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reply [#permalink] New post 29 Aug 2007, 21:22
step 1) prime factorize 441 into 7, 7, 3, 3

step 2) group 7^2, 3^2

step 3) add one to the power of each exponent: 7^3, 3^3 (looks like)

step 4) easily multiply exponents to arrive at # of factors

3*3= 9 possible of 441

:) cool huh, I learned that on this website: You can learn a lot here as well I am sure! best luck. . .

You know this means that there are 9 possible factor combinations of the smallest prime factors of 441.
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Re: reply [#permalink] New post 29 Aug 2007, 21:32
mww7786 wrote:
step 1) prime factorize 441 into 7, 7, 3, 3

step 2) group 7^2, 3^2

step 3) add one to the power of each exponent: 7^3, 3^3 (looks like)

step 4) easily multiply exponents to arrive at # of factors

3*3= 9 possible of 441

:) cool huh, I learned that on this website: You can learn a lot here as well I am sure! best luck. . .

You know this means that there are 9 possible factor combinations of the smallest prime factors of 441.

1 = 1
3*3 = 9
7*7*3 = 147
7*7 = 49
3*7 = 21
3*3*7 = 63
3*3*7*7 = 441
3 = 3
7 = 7

mww7786 - nice method ! thanks !

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 [#permalink] New post 29 Aug 2007, 23:40
Prime factorization first! 441 = 63 * 7 = 7*9*7 = 7^2 * 3^2

For 7 there are 3 possibilites (to the power of 0,1 and 2)
For 3, there are 3 possibilites (to the power of 0,1 and 2)

Total number of factors = 3*3 = 9
  [#permalink] 29 Aug 2007, 23:40
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