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*378#
Even, divide by 2: #756=2*2*189#
Odd, so try 3: #756=2*2*3*63#
And again: #756=2*2*3*3*21#
And again: #756=2*2*3*3*3*7#
7 is a prime, so you're finished.

You write the result as #756=2^2*3^3*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.