4.3 Notes- GCF
Greatest common factor: the largest of the common factors of two or more numbers. Also known
as “GCF”.
Method 1: List the factors
Ex. 16: 1, 2, 4, 8, 16
24: 1, 2, 3, 4, 6, 8, 12, 24
8 is the largest number that will go into
both, so 8 is the GCF
Method 2: Use prime factorization
Ex. 12: 2 x 2 x 3
24: 2 x 2 x 2 x 3
32: 2 x 2 x 2 x 2 x 2
a. write the prime factorization of each number
b. find the common prime factors
c. find the product of those prime factors
2 x 2 = 4 (since each number has two ‘2s’ in common, 4 would be the GCF)
Ex. There are 12 boys and 18 girls in Mr. Ruiz’s science class. The students must form lab groups.
Each group must have the same number of boys and the same number of girls. What is the
greatest number of groups Mr. Ruiz can make if every student must be in a group?
*Whenever you see ‘greatest number of groups’, that means to find the greatest common
factors of the number*
Ex. 12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9, 18
Since 6 is the GCF, that means there will be 6 groups
**Draw a picture to check:
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