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

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Director
Joined: 03 Jul 2003
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What is the easy way to find all the factors that are [#permalink]  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
Joined: 23 Sep 2003
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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.
Manager
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Try elimination.. [#permalink]  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
Senior Manager
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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
Manager
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look closer.. [#permalink]  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
Senior Manager
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right, that was a typo on my part.
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