Monomials and
Factoring
Honors Math – Grade 8
KEY CONCEPT
Prime and Composite Numbers
A whole number, greater than 1, for which the only factors are
1 and itself is called a prime number.
Examples: 2, 3, 4, 5, 11, 13, 17, 19
A whole number, greater than 1, that has more than two
factors is called a composite number.
Examples: 4, 6, 8, 9, 10, 12, 14, 15, 200
0 and 1 are NEITHER prime nor composite.
Find the prime factorization of 90
90
Make a factor tree
What are some
factors of 90 that
are not prime?
9
10
Are 9 and 10 prime?
Write factors for
each number that
is composite.
Circle the prime
numbers.
3
2
35
90  2  3  5
2
A whole number expressed as the product of prime numbers is called the prime factorization of the number.
Recall: factors are numbers multiplied to obtain a product.
Factor the monomial completely
A monomial is in factored
form when it is expressed as
the product of prime numbers
and variables, and no
variable has an exponent
greater than 1.
-12 = -1 x 12
12 = 2 x 2 x 3
Write the
prime
factorization
of 12.
Write the
exponents in
expanded
form.
 12a b  1  12a b
2 3
 1  2  2  3a b
2 3
2 3
 1 2  2  3  a  a  b  b  b
Find the GCF of 48 and 60
Write the prime factorization
of each number. “Factor”
each number.
Circle the common prime
factors.
The common prime factors
are 2, 2, and 3.
The product of the
common prime factors is
called the greatest
common factor (GCF).
48
4 12
2 23 4
2 2
60
5 12
3 4
2 2
48  2  2  2  2  3
60  5  3  2  2
The GCF of 48 and 60 = 2 x 2 x 3 = 12
KEY CONCEPT
Greatest Common Factor (GCF)
The GCF of two or more monomials
is the product of their common
factors when each monomial is
written in factored form.
If two or more integers or monomials
have a GCF of 1, then the integers
or monomials are said to be
relatively prime.
2
2
Find the GCF 36 x y & 54 xy z
Factor each number.
36 x y  2  2  3  3  x  x  y
2
54 xy z  2  3  3  3  x  y  y  z
2
Circle the common prime
factors.
The GCF is the product of common
prime factors.
GCF  2  3  3  x  y  18 xy
Find the GCF 17d
3
&
5d
2
Factor each number.
17d  1  17  d  d  d
3
5d  1  5  d  d
2
Circle the common prime
factors.
The GCF is the product of common
prime factors.
GCF 1 d  d  d
2
GCF
2
2 2
3 3
42a b,6a b ,18a b
Factor each number.
42a b  2  3  7  a  a  b
2 2
6a b  2  3  a  a  b  b
3 3
18a b  2  3  3  a  a  a  b  b  b
2
Circle the common prime
factors.
The GCF is the product of common
prime factors.
GCF  2  3  a  a  b  6a b
2