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What is the easy way to find all the factors that are

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Director
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What is the easy way to find all the factors that are [#permalink] New post 17 Mar 2004, 09:18
What is the easy way to find all the factors that are between 6 and 120, both inclusive, for 240?

One way is to write all the factors and pick only those that statisfy this
condition. Is there any other better way?
Senior Manager
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 [#permalink] New post 17 Mar 2004, 10:51
Well, I can only think about one other method although I'm not sure if it's necessarily faster.

240 = 2^4*3*5

2*3 = 6
2^3*3*5 = 120

So you can try different combo's of anything between 2*3 and 2^3*3*5. So I guess you can use the combinations formula to figure that out but this sounds like a longer method.
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Try elimination.. [#permalink] New post 17 Mar 2004, 11:06
240 = 2^4*3*5

# of factors for 240 = 5*2*2 = 20

Less factors that are not between 6 nd 120: 1, 2, 3, 4, 5 and 240 = 6

Factors between= 20-6 = 14
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 [#permalink] New post 17 Mar 2004, 11:14
Mantha,

You said: "# of factors for 240 = 5*2*2 = 20 "

How did you get 5, 2 and 2? Did you add 1 to each raised exponent?

I.E. 4 + 1 = 5
0 + 1 = 1
0 + 1 = 1
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look closer.. [#permalink] New post 17 Mar 2004, 11:31
You said: "# of factors for 240 = 5*2*2 = 20 "

How did you get 5, 2 and 2? Did you add 1 to each raised exponent?

I.E. 4 + 1 = 5
1+1 = 2 not 0 + 1 = 1
1+1 = 2 not 0 + 1 = 1
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 [#permalink] New post 17 Mar 2004, 11:37
right, that was a typo on my part.
  [#permalink] 17 Mar 2004, 11:37
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