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Difficulty Factoring Large Numbers

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Difficulty Factoring Large Numbers

by crisprin117 » Fri Feb 21, 2014 10:00 am
Hello Everyone,

This is my first post and I just want to say hi and thank you for the community.

I happen to believe that the math portion of the gmat is my stronger section but I continually have difficulty in factoring large numbers. Whether it is errors in arithmetic or not, my method takes too much time or yields indivisible situations that should not occur. Any ideas?

Thanks
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by [email protected] » Fri Feb 21, 2014 11:15 am
Hi crisprin117,

The speed with which you can factor a number (especially a big number) is based a bit on your math "skill" and a bit on your pattern-matching ability. Since the Quant section of the GMAT is NOT a "math test" (even though you'll do lots of small calculations), you have to focus more on the pattern-matching and less on the division.

To that end, it helps if you know the quick ways to identify if a number is divisible by 2, 3, 4, 5, 6 or 9. In addition, it's almost always faster to write down a calculation and do the work by hand than to stare off into space and try to do it in your head. Many pacing problems are caused simply because the Test Taker opts not to write things down.

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by crisprin117 » Mon Feb 24, 2014 7:48 am
Hey,

Thanks for the advice. I think I will just have to set aside time specifically for this topic.
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by Bill@VeritasPrep » Mon Feb 24, 2014 12:56 pm
I find that just doing more math on a daily basis tends to be a big help. Go grocery shopping and keep a running total in your head. You're driving, and LA is 133 miles away...that's 19*7 miles. The more you do it, the more you'll start to make those connections and find shortcuts that make sense to you.
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by ceilidh.erickson » Sat Mar 01, 2014 1:15 pm
A good general rule on the GMAT is: if you're doing too much computation, you're probably doing something wrong! Most GMAT questions can be solved with minimal computation. For example, if you're given:
(27 x 32 x 36)/(64 x 81)
Don't multiply these together to create big numbers, then try to divide! First, break them down into smaller numbers. We can break all of these into factors of 2 and 3, and then easily cancel:
(3^3 x 2^5 x 2^2 x 3^2)/(2^6 x 3^4)
Then simplify: 3^1 x 2^1 = 6

Always simplify first, and you very rarely end up with big numbers to factor.

But when you do have to factor, here are those divisibility rules that Rich was talking about:
x is divisible by:

2 if x is even

3 if the sum of the digits is divisible by 3. 183 is divisible by 3 because 1 + 8 + 3 = 12

4 if x is divisible by 2 twice, or if the last two digits are divisible by 4. 43,524 is divisible by 4 because 24 is divisible by 4.

5 if x ends in a 0 or 5

6 if x is divisible by 2 and 3

8 if x is divisible by 2 three times

9 if the sum of the digits is divisible by 9

10 if x ends in 0
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by garmahis » Mon Jun 09, 2014 12:37 am
Hi crisprin117,

I can feel you. I used to be on the same plate. I had the same problems before but practice makes perfect. There's no clean cut formula on how to to factor out large numbers. It's pretty tedious a problem to be solved in a minute or so. I agree with Bill, practice factoring numbers every day until this becomes a habit. When the test arrives, your brain is already primed to factoring numbers and it will be easier than it used to be. I'm wishing you all the luck. Keep practicing. You will surely succeed if you have the will.

Best,

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