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 April 11th, 2018, 05:29 AM #1 Member   Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0 How can you find the factors of a number easily? How can you find the factors of a number easily? It is probably by prime factorisation, but I am not sure how prime factorisation can be used to find factors. Please help! Thanks! April 11th, 2018, 06:28 AM   #2
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Quote:
 Originally Posted by Student2018 How can you find the factors of a number easily? It is probably by prime factorisation, but I am not sure how prime factorisation can be used to find factors. Please help! Thanks!
First, try dividing by 2 as many times as it will divide.

Then try dividing by 3, by 5, by 7, etc.

For example:756.
$\displaystyle 756 \div 2 = 378$

$\displaystyle 378 \div 2 = 189$

$\displaystyle 189 \div 2 = 94.5$

*So we have 2 factors of 2.

$\displaystyle 189 \div 3 = 63$

$\displaystyle 63 \div 3 = 21$

$\displaystyle 21 \div 3 = 7$

$\displaystyle 7 \div 3 = 2.333333$

*So we have 3 factors of 3.

$\displaystyle 7 \div 5 = 1.4$

*So we have no factors of 5.

$\displaystyle 7 \div 7 = 1$

*So we have 1 factor of 7.

Combing the statements in * we have that $\displaystyle 756 = 2^2 \cdot 3^3 \cdot 7$

-Dan April 11th, 2018, 06:32 AM   #3
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Quote:
 Originally Posted by Student2018 How can you find the factors of a number easily? It is probably by prime factorisation, but I am not sure how prime factorisation can be used to find factors. Please help! Thanks!
You are correct.

To find all possible factors of an integer, start by doing a prime factorization of the absolute value of the integer in question. Then take 1, those prime factors, and all possible multiples of those factors both plus and minus to find all possible factors.

Example. 196 = 2 * 98 = 2 * 2 * 49 = 2 * 2 * 7 * 7.

So the possible factors are

$\pm 1,\ \pm 2,\ \pm 7,\ \pm 4,\ \pm 14,\ \pm 49,\ \pm 28,\ \pm 98,\ \pm 196.$ Tags easily, factors, find, number Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ishaanmj007 Number Theory 2 May 14th, 2015 05:07 PM MATHEMATICIAN Number Theory 15 August 26th, 2013 10:16 PM rnck Advanced Statistics 4 June 21st, 2013 04:26 PM mathbalarka Number Theory 15 June 15th, 2012 07:36 PM jdraughn Elementary Math 4 November 25th, 2009 09:59 AM

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