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How many of the factors of 72 are divisible by 2? 4 5 6

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How many of the factors of 72 are divisible by 2? 4 5 6 [#permalink] New post 21 Nov 2007, 07:07
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How many of the factors of 72 are divisible by 2?

4
5
6
8
9

Is there a shortcut to this question? It is rather tedious to list out all factors of 72
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 [#permalink] New post 21 Nov 2007, 07:32
Expert's post
E.

72=2^3*3^2

N0=(3+1)(2+1)=12 - numbers of all factors

N1=(2+1)=3 - numbers of all factors that are not divisible by 2

Therefore, 12-3=9

9.
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 [#permalink] New post 23 Nov 2007, 12:28
bmwhype2 wrote:
walker wrote:
E.

72=2^3*3^2

N0=(3+1)(2+1)=12 - numbers of all factors

N1=(2+1)=3 - numbers of all factors that are not divisible by 2

Therefore, 12-3=9

9.


Can you explain the logic of that?


lets say we have some random number N and its factors are
2^4 * 5^2 *7^2

The number of factors that are not divisible by 2 are 3*3=9?
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 [#permalink] New post 24 Nov 2007, 09:34
bmwhype2 wrote:
bmwhype2 wrote:
walker wrote:
E.

72=2^3*3^2

N0=(3+1)(2+1)=12 - numbers of all factors

N1=(2+1)=3 - numbers of all factors that are not divisible by 2

Therefore, 12-3=9

9.


Can you explain the logic of that?


lets say we have some random number N and its factors are
2^4 * 5^2 *7^2

The number of factors that are not divisible by 2 are 3*3=9?


Any answers on this? Thought I should keep this alive (:
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 [#permalink] New post 25 Nov 2007, 02:23
bmwhype2 wrote:
bmwhype2 wrote:
walker wrote:
E.

72=2^3*3^2

N0=(3+1)(2+1)=12 - numbers of all factors

N1=(2+1)=3 - numbers of all factors that are not divisible by 2

Therefore, 12-3=9

9.


Can you explain the logic of that?


lets say we have some random number N and its factors are
2^4 * 5^2 *7^2

The number of factors that are not divisible by 2 are 3*3=9?


I think so.
1
5
7
5*5
7*7
5*7
5*5*7
7*7*5
5*5*7*7

If this is proven to be a general rule, is very very useful.
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 [#permalink] New post 28 Nov 2007, 04:40
bmwhype2 wrote:
bmwhype2 wrote:
walker wrote:
E.

72=2^3*3^2

N0=(3+1)(2+1)=12 - numbers of all factors

N1=(2+1)=3 - numbers of all factors that are not divisible by 2

Therefore, 12-3=9

9.


Can you explain the logic of that?


lets say we have some random number N and its factors are
2^4 * 5^2 *7^2

The number of factors that are not divisible by 2 are 3*3=9?


think i made a mistake.

its 5*3*3 = 45 total factors
45 - (3 + 3) = 26
  [#permalink] 28 Nov 2007, 04:40
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How many of the factors of 72 are divisible by 2? 4 5 6

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