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April 11th, 2018, 06:29 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, 07:28 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,915 Thanks: 774 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
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, 07:32 AM  #3  
Senior Member Joined: May 2016 From: USA Posts: 1,206 Thanks: 494  Quote:
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 $\pm 1,\ \pm 2,\ \pm 7,\ \pm 4,\ \pm 14,\ \pm 49,\ \pm 28,\ \pm 98,\ \pm 196.$  

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