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# How do we do this one

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How do we do this one [#permalink]  11 Mar 2009, 20:21
How many factors that are not mutiples of 6 exist in 264,600 ?

Any cool way math guru's
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Re: How do we do this one [#permalink]  11 Mar 2009, 20:48
Allana25 wrote:
How many factors that are not mutiples of 6 exist in 264,600 ?

Any cool way math guru's

264,600 = 2^3*3^3*5^2*7^2

total number of factors = (3+1)*(3+1)*(2+1)*(2+1) = 144

264,600 = 2^3*3^3*5^2*7^2 = (3*2) *(2^2*3^2*5^2*7^2 )
==(6) *(2^2*3^2*5^2*7^2 )

No of factors that are divisble by 6 = 3*3*3*3= 81

Ans = 144-81 = 63
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Re: How do we do this one [#permalink]  11 Mar 2009, 21:48
I didn't get one part ... why did you take out the 6... sorry if my question is silly...

Thanks again
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Re: How do we do this one [#permalink]  12 Mar 2009, 15:21
Allana25 wrote:
I didn't get one part ... why did you take out the 6... sorry if my question is silly...

Thanks again

You have to find the multiples of 6 i.e. number of the forms: 6 * x. That's why 6 was taken out and all the possible values of x were calculated by applying the original formula i.e.

number of factors for p^a * q^b * r^c (where p,q,r are prime numbers) is = (a+1) * (b+1) * (c+1)

Hope this helps.
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Re: How do we do this one [#permalink]  15 Mar 2009, 01:58
Didnt know about such a formula at all.

Thanks a lot!
Re: How do we do this one   [#permalink] 15 Mar 2009, 01:58
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