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abhirup1711: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Wed Jul 13, 2011 2:27 pmFollowed by: 2 members

by abhirup1711 » Tue Oct 02, 2012 1:00 am

Hi,
I can't remember the rule that dividing a particular numbers into its prime factors and then adding 1 gives some kind of a solution. Can someone please help me out? Apologies for being so vague.

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Source: Beat The GMAT — Problem Solving | Tue Oct 02, 2012 1:00 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue Oct 02, 2012 2:46 am

I think you might be asking about how we count how many divisors a number has. If you take a number like 375, and want to work out how many positive divisors 375 has, you can first prime factorize:

375 = 3*125 = (3^1)(5^3)

Now to find how many positive divisors 375 has in total, we can add 1 to each exponent and multiply what we get. So 375 has 2*4 = 8 divisors.

If you want to know why this works, or to see other examples, I and other experts here have posted about this method a few times, so you'll find more detail by searching the forum for a phrase like 'counting divisors'.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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