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18 Jun 2020, 11:33
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Hello GMATCLUB users!
I hope we can help each other find more efficient ways to divide by large numbers (it also applies to prime factorization).
I am struggling with dividing large numbers by a two-digit numbers AND/OR small numbers (for factorization).
For example:
\(\frac{1416}{3} \)
Sometimes I have those questions where I need to find the prime factorization of such expression and/or I need to divide those numbers by 1 to 2-digit numbers as part of the question - and it just takes a LOT of time.
What techniques do you guys use?
*I tried to search this topic, but couldn't find any threads.
I hope we can help each other find more efficient ways to divide by large numbers (it also applies to prime factorization).
I am struggling with dividing large numbers by a two-digit numbers AND/OR small numbers (for factorization).
For example:
\(\frac{1416}{3} \)
Sometimes I have those questions where I need to find the prime factorization of such expression and/or I need to divide those numbers by 1 to 2-digit numbers as part of the question - and it just takes a LOT of time.
What techniques do you guys use?
*I tried to search this topic, but couldn't find any threads.
yashikaaggarwal
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18 Jun 2020, 12:37
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You could save time by analyzing whether the number is first divisble by the no. Or not.
If the number is divisible,
You could simply learn the rules of divisibility.
Such as in your example.
1416/3
For divisibility rule of 3 add no. 1+4+1+6 = 12 = 1+2 => 3
Which is divible by 3
1416/3 => 472
You can learn further divisibility rule with the help of following link : https://gmatclub.com/forum/divisibility ... l#p1098760
If the no. is not divisible by no., you can use divisibility theorem , I.e, Euler's Theorem, Chinese Theorem etc. Just search Remainder theoram on google you will find some shortcuts to solve such division questions easily.
Posted from my mobile device
If the number is divisible,
You could simply learn the rules of divisibility.
Such as in your example.
1416/3
For divisibility rule of 3 add no. 1+4+1+6 = 12 = 1+2 => 3
Which is divible by 3
1416/3 => 472
You can learn further divisibility rule with the help of following link : https://gmatclub.com/forum/divisibility ... l#p1098760
If the no. is not divisible by no., you can use divisibility theorem , I.e, Euler's Theorem, Chinese Theorem etc. Just search Remainder theoram on google you will find some shortcuts to solve such division questions easily.
Posted from my mobile device
18 Jun 2020, 18:46
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yashikaaggarwal
Hi, thank you for a fast response.
Yes, I do know the divisibility rules. But say, like in the example I presented, that you know the number is divisible by 3. Good for you, it still takes time to complete the division.
-What about two digit-numbers? It'll take even more time.
*I am usually struggling when I encounter those questions that ask about LCM of two different numbers and whether another value (say Z), is divisible by both of them or something like this - I can definitely look for a real example.
What I'm saying is that 2 minutes is sometimes not enough for all of those intermediary calculations. There's gotta be a way to factorize/divide quicker!
