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09 Sep 2010, 19:07
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I've noticed this with the MGMAT books so far, I think they do the best at really explaining in writing many different ways of tackling a difficult problem, but I'm lost at how they just write out a simple step like its part of the solution with no mention of how they got it so quickly at least somewhere in one of their books. It seems as they expect you to know a shortcut already that maybe I'm just not seeing. Has anyone else experienced this? Particularly in the following areas:
Prime Factorization - for example as part of explanation on a more advanced topic they write something like "For instance 9,450 = 2^1 x 3^3 x 5^2 x 7^1, therefore... huh? There is no prior mention of that number in the paragraph. I'm used to the factor tree method, but think that would still take me more time than just writing it as if it is an already known fact. Is there a shortcut way to find all the powers of the primes of a large # like that without any thought?
There's more examples of different problem types, that I cannot remember off the top of my head right now, but as I'm going back through these I will edit, hopefully get a list going of efficient shortcuts for simple steps in more difficult problems.
Prime Factorization - for example as part of explanation on a more advanced topic they write something like "For instance 9,450 = 2^1 x 3^3 x 5^2 x 7^1, therefore... huh? There is no prior mention of that number in the paragraph. I'm used to the factor tree method, but think that would still take me more time than just writing it as if it is an already known fact. Is there a shortcut way to find all the powers of the primes of a large # like that without any thought?
There's more examples of different problem types, that I cannot remember off the top of my head right now, but as I'm going back through these I will edit, hopefully get a list going of efficient shortcuts for simple steps in more difficult problems.
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09 Sep 2010, 20:55
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Michmax3
Knowing divisibility rules can help a lot in prime factorization.
Divisibility Rules
2 - If the last digit is even, the number is divisible by 2.
3 - If the sum of the digits is divisible by 3, the number is also.
4 - If the last two digits form a number divisible by 4, the number is also.
5 - If the last digit is a 5 or a 0, the number is divisible by 5.
6 - If the number is divisible by both 3 and 2, it is also divisible by 6.
7 - Take the last digit, double it, and subtract it from the rest of the number, if the answer is divisible by 7 (including 0), then the number is divisible by 7.
8 - If the last three digits of a number are divisible by 8, then so is the whole number.
9 - If the sum of the digits is divisible by 9, so is the number.
10 - If the number ends in 0, it is divisible by 10.
11 - If you sum every second digit and then subtract all other digits and the answer is: 0, or is divisible by 11, then the number is divisible by 11.
Example: to see whether 9,488,699 is divisible by 11, sum every second digit: 4+8+9=21, then subtract the sum of other digits: 21-(9+8+6+9)=-11, -11 is divisible by 11, hence 9,488,699 is divisible by 11.
12 - If the number is divisible by both 3 and 4, it is also divisible by 12.
25 - Numbers ending with 00, 25, 50, or 75 represent numbers divisible by 25.
Applying above rules to prime factorization of 9,450:
We can quickly spot that this number is divisible by 25=5^2 as it ends with 50, by 9 as sum of its digits is divisible be 9=3^2 (9+4+5=18), by 2 as it's ends with 0 --> so it's divisible by 25*9*2=450 --> 9,450/450=21 --> 21=3*7, so we have one more 3 and new prime factor 7 --> 9,450=2*3^3*5^2*7.
Shouldn't take more than 1 minute.
For more on similar issues check Number Theory chapter of Math Book (link in my signature).
Hope it helps.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
