Transcript File

Definitions:
Common Factors – Are factors shared by two or more whole
numbers.
Greatest Common Factor (GCF) – Is the largest common factor
shared between two or more whole numbers.
Method 1: Finding The GCF by Listing the Factors
Example 1: Find the GCF of 16 and 24 by listing the factors.
Factors of 16: 1, 2, 4, 8, and 16
Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
8 is the largest common factor; therefore, it is the GCF of 16
and 24.
Method 2: Finding The GCF by Using Prime Factorization
Example 2: Find the GCF of 40 and 12 by using prime
factorization.
40
12
5
8
2
6
4
2
5•2•2•2
3
2
2
2
3•2•2
2•2=4
Prime Factorization
Product of the common prime
numbers. 4 is the GCF.
Method 3: Finding The GCF by Using a Table
Example 3: Find the GCF of 45 and 75 by making a table.
Prime
Numbers
3
45
5
3 • 5 = 15
75
15
25
3
5
Multiply the prime numbers.
15 is the GCF of 45 and 75.
Find the GCF of the following whole numbers by using prime
factorization.
1.) 45 and 18
2.) 36 and 84
Find the GCF of the following whole numbers by using the table.
1.) 28 and 42
2.) 18, 27, and 30
Real-Life Application
There are 12 boys and 18 girls in Ms. Ruiz’s science class. The students
must form lab groups. Each group must have the same number of boys
and girls. What is the greatest number of groups Ms. Ruiz can make if
every student must be in a group?