Download 4.2 Factors and Prime Factorization

4.2 Factors and Prime Factorization
Learn to write prime factorizations of
composite numbers.
Vocabulary
factor
prime factorization
Prime Number Brain Pop
Whole numbers that are multiplied to
find a product are called factors of that
product. A number is divisible by its
factors.
2 3=6
6÷3=2
Factors
6÷2=3
Product
6 is divisible
by 3 and 2.
Helpful Hint
When the pairs of factors begin to repeat,
then you have found all of the factors of
the number you are factoring.
Additional Example 1A: Finding Factors
List all of the factors of the number 16.
A. 16
16 = 1 • 16
16 = 2 • 8
16 = 4 • 4
16 = 8 • 2
1 2 4
4
1
2
3
4
5
6
7
8
is a factor.
is a factor.
is not a factor.
is a factor.
is not a factor.
is not a factor.
is not a factor.
and 2 have already been listed so stop here.
8 16
You can draw a diagram to illustrate the
factor pairs.
The factors of 16 are 1, 2, 4, 8, and 16.
Additional Example 1B: Finding Factors
List all of the factors of the number 19.
B. 19
19 = 1 • 19
19 is not divisible by any
other whole number.
The factors of 19 are 1 and 19.
You can use factors to write a number
in different ways.
Factorization of 12
1 • 12
2•6
3•4
3•2•2
Notice that
these factors
are all prime.
Prime factorization A way to write a
composite number as the product of prime
factors.
Additional Example 2A: Writing Prime Factorizations
Write the prime factorization of 24.
Method 1: Use a factor tree.
Choose any two factors of 24 to begin. Keep finding
factors until each branch ends at a prime factor.
24
2
•
24
2
•
6
12
•
6
2
•
3
3
•
2
4
2
•
2
24 = 3 • 2 • 2 • 2
24 = 2 • 2 • 2 • 3
The prime factorization of 24 is 2 • 2 • 2 • 3, or 23 • 3.
Check It Out: Example 2A
Write the prime factorization of 28.
Method 1: Use a factor tree.
Choose any two factors of 28 to begin. Keep finding
factors until each branch ends at a prime factor.
28
2
•
28
14
2
•
7
7
28 = 2 • 2 • 7
•
4
2
•
2
28 = 7 • 2 • 2
The prime factorization of 28 is 2 • 2 • 7, or 22 • 7 .
Prime factor this number
12
3 x 4 = 12
3 x 2 x 2 = 12
2 x2 2 x 3 = 12
2 x 3 = 12
Prime factor this number
14
2 x 7 = 14
Prime factor this number
18
3 x 6 = 18
3 x 2 x 3 = 18
2 x 3 x 3 = 18
2
2 x 3 = 18
Watch…….
Factoring Brain Pop