# Which methods of factoring do you use to factor completely?

##### 1 Answer
Jan 5, 2015

You (try to) divide your number by successive primes $2 , 3 , 5 , 7 , 11. . .$

Example :
Say you want to factor $756$
Even number, divide by 2: $756 = 2 \cdot 378$
Even, divide by 2: $756 = 2 \cdot 2 \cdot 189$
Odd, so try 3: $756 = 2 \cdot 2 \cdot 3 \cdot 63$
And again: $756 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 21$
And again: $756 = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 7$
7 is a prime, so you're finished.

You write the result as $756 = {2}^{2} \cdot {3}^{3} \cdot 7$

Remark :
You never have to try a prime that is larger than the square root of the number left, because if that would divide evenly, the result is a smaller number, and you would have already tried that.