Determining factorizations of a number

Question

Now, this might be very easy to a lot of people, but it's one of the things that really slows me down and I need to figure out a way to speed this up. For example.

A, B, and C are positive integers greater than 1. If A<B<C and abc = 286, what is c-b?

I understand how to do the problem. 
 What you must do is break up 286 into it's prime factorizations, in this case, 2, 11, and 13. At that point it should be very easy to solve the problem. I can very easily determine that 286 is divisible by 2, yet figuring out that 143 is 11 x 13 is my problem; it's a large, unwieldy number that poses a significant time sync for me. BTW, the answer to the question is 2.

For figuring out larger multiples such as that, do you guys have any tips or tricks?

nverma · Answer

Factorization is the quickest way..!!
To find the factor of a given (no. in this case 143) it's important to know whether a given no.(143) is a prime no..??

If it's a prime no..then there can be only two factors 1 and the number itself..
otherwise look for the factors...

Check for prime.

Find the approximate square root of the number (143)...
the square root should lie between 11 and 12..!! as  11^2  is 121 and  12^2  is 144...
then look for all the prime numbers less than 11.. in this case 2,3,5,7,11
and check whether the given no. (143) is divisible by any of these (2,3,5,7,11)..If it's divisible..then the no. is not prime..!! and any one or more of these numbers are its factors..

BUT, if the number is not divisible then the number is prime...!!
so 143 is divisible by 11...

In this way, we don't blindly look for all the factors of a given number..

Take example of 149... Its square root should lie between 12 and 13..
Try dividing 149 by all the prime numbers less than 12 >>>> 2,3,5,7,11... and u will find it's not divisible by any of these prime numbers...So 143 is prime..

Hope it helps..!!

mmphf · Answer

Awesome technique! Thanks! +1 for you!

Dartastic · Answer

That's a great help! Thanks!

dixitraghav · Answer

what i would suggest you is to do lot of math questions so that will definately help you in remembering most common factors , roots LCM of few no. ,avg etc, and that will help you to quickly solve these sort of problems.

dixitraghav · Answer

valuable trick provided nverma thanks & kudos

PTK · Answer

Typos, instead of 143 , you probably have meant 149.

nikheel · Answer

Knowing the tests for divisibility for the basic primes (2, 3, 5, 7, 11) would also help. Take 143 for example, numbers divisible by 11 have alternate digits adding to be the same (or sums differ by a multiple of 11) here: 1+3=4. So keep dividing it up, use a<b<c and voila, you have a, b, c.

The advantage with GMAT quant is that it wont give numbers that are too hard to factorize, nor multiples of primes 13 and above.

seku · Answer

cool.. this wud be a great help. thanx :-D

GMATBLACKBELT720 · Answer

Nice. Another point in the problem is that it specifically states that three numbers are all greater than 1. So when you get to 143 and 2, you know that 143 cannot be prime.

Determining factorizations of a number

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards