Objectives The student will be able to: find the greatest common factor (GCF) for a set of monomials.

The Greatest Common Factor (GCF) of 2 or more numbers is the largest number that can divide into all of the numbers. 4) Find the GCF of 42 and 60. Write the prime factorization of each number.

4) Find the GCF of 42 and 60. = 2 • 3 • 7 60 = 2 • 2 • 3 • 5 = 2 •  3 • 7 60 = 2 • 2 • 3 • 5 What prime factors do the numbers have in common? Multiply those numbers. The GCF is 2 • 3 = 6 6 is the largest number that can go into 42 and 60!

What is the GCF of 48 and 64? 2 4 8 16

Think Backwards… Find Factors Circle Common Factors Group Greatest Factor

Step 1: Find the Factors 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36

Step 2: Circle Common Factors 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36

Step 3: Group the Greatest Factor 24 – 1,2,3,4,6,8,12,24 36 – 1,2,3,4,6,9,12,18,36

The Greatest Common Factor of 24 and 36 is… 12

The Greatest Common Factor of 24 and 36 is… 12

What is the GCF of 18 and 27? 18 27 Factors of 18: 1, 2, 3, 6, 9, 18 1 x 18 1 x 27 2 x ? 2 x 9 3 x 9 3 x 6 Factors of 27: 1, 3, 9, 27 4 x ? 5 x ? 4 x ? 6 x ? 5 x ? 7 x ? Common Factors: 1, 3, 9 8 x ? 6 x 3 9 x 3 GCF: 9

Ex: Find the GCF(24, 40) Prime Factorizations 12 2 20 2 6 2 10 2 3 2 5 24 = 2 * 2 * 2 * 3 40 = 2 * 2 * 2 * 5

Ex: Find the GCF(32, 51) Prime Factorization: 16 3 17 2 8 2 4 51 = 3 * 17 2 2 32 = 2 * 2 * 2 * 2 * 2

Ex: Find the GCF(102, 84) Prime Factorization: 51 2 42 3 17 2 21 3 7 32 = 2 * 3 * 17 51 = 2 * 2 *3 * 7