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.