Page 872 - Algebra 1

Prime and Composite Numbers and Prime Factorization
Skills Bank Lesson 12
A prime number is a number that has exactly two factors, 1 and itself. For example, 5 is a prime number because its only factors are 1 and 5.
A composite number has more than two factors. For example, 8 is a composite number because its factors are 1, 2, 4, and 8.
The number 1 is neither prime nor composite.
Determining Whether a Number is Prime or Composite
Determine whether each number is prime or composite.
Example
1
a. 18
SOLUTION
1, 2, 3, 6, 9, 18
18 is a composite number.
b. 13
SOLUTION
1, 13 List the factors. 13 is a prime number.
List the factors.
Every composite number can be written as the product of two or more prime numbers. This product is called the prime factorization of a number.
Using a Factor Tree to Find the Prime Factorization
Example
2
36
SOLUTION
36 Choose any two factors of 36. Continue to factor until each branch ends in
3 12 34
22
a prime number.
Theprimefactorizationof 36is2·2·3·3or22 ·32.
Skills Bank Practice
Determine whether each number is prime or composite.
a. 17 b. 15
Find the prime factorization of each number. e. 72 f. 28
i. 76 j. 32
c. 32 g. 34
k. 45
d. 29 h. 24
l. 52
Skills Bank 857
SKILLS BANK