Notes for Lesson 8-1: Factors and Greatest Common Factors
8-1.1 – Writing Prime Factorization
The whole numbers that multiply to find a product are called factors. A number is divisible by its factors. The
prime factorization of a number is the factors that are all prime numbers. We can find the prime factorization
of a number by using a factor tree or a ladder diagram.
Examples: Write the prime factorization of each number.
Show both methods
60
2  2  3 5
40
2 2 25
150
2  3 5 5
22  3 5
23  5
2  3  52
8-1.2 – Finding the GCF of numbers
Factors that are shared by two or more numbers are called common factors. The greatest of these factors is
called the greatest common factor or GCF. You can either list all of the factors to see what factors are in
common or more efficiently use the prime factorization of the numbers and take the common prime factors to
find the GCF.
Examples: Find the GCF of each pair of numbers.
18 and 27
24 and 60
24  2  2  2  3 or 2  3
18  2  3  3 or 2  32
60  2  2  3  5 or 2 2  3  5
Common are 2  2  3  12
The GCF is 12
27  3  3  3 or 33
Common are 3  3  9
The GCF is 9
3
8-1.3 – Finding the GCF of monomials
You can also find the GCF of monomials that contain variables. To find the GCF of monomials, write the
prime factorization of each coefficient and take the smaller of each common variable.
Examples: Find the GCF
3 x 3 and 6 x 2
33
6  23
15 x 3 y 2 and 9 x 2 y 3
15  3  5
2
3 is common and x is smaller so
the GCF is 3 x
2
9  3 3
3 is common and x 2 is the