Pre Algebra (Period 2 & 4)

Prime Factorization & GCF 4-3


Prime Factorization
Now that you know what a number divides by, 
you can get its prime factorization


Prime = a number with exactly 2 factors (itself and 1)


Composite = a number with at least 3 factors


1 and 0 are neither composite nor prime


How do you find all the prime factors of a number?

You learned Factor Trees in previous years and Factor Trees are a good strategy

Make sure you take all the bottom factors only!


EXAMPLE: 54




The prime factorization of 54 = 2x3x3x3 or 2(3³)


Make sure you list the factors from least to greatest!

There are multiple Factor Trees based on what you decide to use as your first 2 factors. But each one will get you to the same "bottom" of the tree.

The prime factorization of 54 IS ALWAYS = 2x3x3x3 or 2(3³) no matter how you start your Factor Tree

You can also use something called INVERTED DIVISION.

This is similar to Factor Trees but you must begin with the SMALLEST PRIME FACTOR that goes into the number and keep using it until it no longer works.

Then you go on to the next higher prime factor, etc.

EXAMPLE: For 54 again, but this time using Inverted Division.


THERE IS ONLY ONE CORRECT FORM OF INVERTED DIVISION!
BUT... the factors will always be in order if you follow the rules!!