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# How to calculate the number of factors of any number? Seems difficult

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Intern
Joined: 15 Oct 2017
Posts: 28
Schools: Northeastern '20
How to calculate the number of factors of any number? Seems difficult  [#permalink]

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07 Mar 2018, 00:41
Thank you!
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Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3631
How to calculate the number of factors of any number? Seems difficult  [#permalink]

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07 Mar 2018, 00:46
1
thegame12 wrote:
Thank you!

Hey thegame12 ,

Basically you are looking for this : https://gmatclub.com/forum/finding-numb ... l#p1297620

Let me know in case of any concern.

Thanks
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Joined: 04 Dec 2015
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Re: How to calculate the number of factors of any number? Seems difficult  [#permalink]

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08 Mar 2018, 12:02
thegame12 wrote:
Thank you!

It depends on how big the number is!

If it's a small number, you can create a factor table and just write out all of the factors. They come in pairs, and the table will look like this:

24
1 x 24
2 x 12
3 x 8
4 x 6

Start with 1 (which is a factor of every integer), and move upwards until you've got all of them. 24 has 8 factors in total. You know you have all of them when moving upwards would give you a factor (in this case, 6) that you already found.

If the number is too big to do this, you can start with the prime factors and figure it out from there. Suppose we're trying to figure out how many factors 2,400 has.

Prime factorization of 2,400 = 2*2*2*2*2*3*5*5

That's five 2s, one 3, and two 5s.

By definition, every factor of 2400 will be made up of some combination of those prime factors. For instance, 2*2*2 is a factor of 2400. So is 2*3*5*5. But 2*3*7 isn't, because it has a 7 in it, and there's no 7 in 2400.

How many ways can you combine those prime factors?

You can use anywhere from zero to all five of the 2s - that's 6 possibilities...
you can either use the 3 or not use it - that's 2 possibilities...
you can use zero, one, or two of the 5s - that's 3 more possibilities.

6*2*3 = 36 factors in total.
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How to calculate the number of factors of any number? Seems difficult  [#permalink]

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13 Mar 2018, 14:45
1
Hello,

The following 2-minutes video will help you find the number of factors of any number. Watch it carefully to understand the concept and to avoid the common mistakes.

Best wishes,
Experts' Global
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How to calculate the number of factors of any number? Seems difficult   [#permalink] 13 Mar 2018, 14:45
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