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# How to find out the # of factors a particular number has?

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Joined: 15 Jun 2011
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How to find out the # of factors a particular number has? [#permalink]

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16 Jun 2011, 05:11
I'm going through the "Number Properties" of the MGMAT books and I was wondering if we were given a certain number, what would be the best way to find out how many unique factors it has? For example, 48 has 10 factors: 1,2,3,4,6,8,12,16,24,48. I'm guessing there a better way than multiplying all the prime factors in various ways. Thanks.

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Re: How to find out the # of factors a particular number has? [#permalink]

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16 Jun 2011, 05:18
Liquidus wrote:
I'm going through the "Number Properties" of the MGMAT books and I was wondering if we were given a certain number, what would be the best way to find out how many unique factors it has? For example, 48 has 10 factors: 1,2,3,4,6,8,12,16,24,48. I'm guessing there a better way than multiplying all the prime factors in various ways. Thanks.

One way is to go on dividing it till u reach the lowest number..
other way is ( you will find it in MGMAT book as well) is getting the prime factors in the form of p^a* q^b.....X^n
where both p and q are prime numbers and the forumma for number of factos is
(a+1)*(b+1)*..................*(n+!)

to illustrate in this ex:
48 can be written as 6*8 = 2*2* 2^3
2^4*3
thus its (4+1)(1+1)= 5*2 = 10
Note that in the above ex: power of 3 is 1

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Re: How to find out the # of factors a particular number has? [#permalink]

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16 Jun 2011, 05:39
prime factors approach is best

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Re: How to find out the # of factors a particular number has? [#permalink]

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16 Jun 2011, 06:32
Thanks for the reply. That formula was what I was looking for.

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Veritas Prep GMAT Instructor
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Location: Pune, India
Re: How to find out the # of factors a particular number has? [#permalink]

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16 Jun 2011, 13:01
Liquidus wrote:
I'm going through the "Number Properties" of the MGMAT books and I was wondering if we were given a certain number, what would be the best way to find out how many unique factors it has? For example, 48 has 10 factors: 1,2,3,4,6,8,12,16,24,48. I'm guessing there a better way than multiplying all the prime factors in various ways. Thanks.

For a detailed discussion on number of factors and how to write them all out, check
http://www.veritasprep.com/blog/2010/12 ... ly-number/
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Re: How to find out the # of factors a particular number has?   [#permalink] 16 Jun 2011, 13:01
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