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Lesson 9-2 Prime Factorization
Prime Number – a whole number that has exactly two factors, 1 and itself
Composite Number – a whole number that has more than two factors
Prime Factorization – representing a number as a product of prime factors
Factor Tree – a diagram used to show all prime factors
Monomial – a number, variable or a product of numbers and variables
Factor – to write a number as a product of its factors
Example 1 Identify Prime and Composite Numbers
Determine whether each number is prime or composite.
a. 41
Find factors of 41 by listing the whole number pairs whose product is 41.
41 = 1  41
The number 41 has only two factors. So, 41 is a prime number.
b. 42
Find factors of 42 by listing the whole number pairs whose product is 42.
42 = 1  42
42 = 2  21
42 = 3  14
42 = 6  7
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Since the number has more than two
factors, it is composite.
Standardized Test Example 2 Write Prime Factorizations
What is the prime factorization of 24?
A 234
B 2  32
C 22  3
D 23  3
Read the Test Item
You are asked to find the factors of 24 that are prime numbers.
Construct a factor tree to find all of the prime factors.
Solve the Test Item
One Way
24
4

Another Way
24
Choose any pair of whole
number factors of 24.
2 
6
12
Continue to factor any
number that is not prime.
2  2 2  3
2  3  4
2  32 2
The prime factorization of 24 is 2  2  2  3 or 2  3. So, the answer is D.
3
Example 3 Factor Monomials
Factor each monomial.
a. 12c3d
12c3d = 2  2  3  c3 d
=223cccd
b. –18ab2
–18ab2 = -1  2  3  3  a  b2
= -1  2  3  3  a  b  b
12 = 2  2  3
3
c d=cccd
-18 = -1  2  3  3
2
ab =abb