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Objectives The student will be able to:

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1 Objectives The student will be able to:
1. find the prime factorization of a number. 2. find the greatest common factor (GCF) for a set of monomials. SOL: A.2c Designed by Skip Tyler, Varina High School

2 A prime number is a number that can only be divided by only one and itself. A composite number is a number greater than one that is not prime. Prime or composite? 37 prime 51 composite

3 Prime or Composite? 89 Prime Composite Both Neither

4 1) Find the prime factorization of 84.
84 = 4 • 21 = 2 • 2 • 3 • 7 = 22 • 3 • 7 2) Find the prime factorization of -210. -210 = -1 • 210 = -1 • 30 • 7 = -1 • 6 • 5 • 7 = -1 • 2 • 3 • 5 • 7

5 3) Find the prime factorization of 45a2b3
45a2b3 = 9 • 5 • a • a • b • b • b = 3 • 3 • 5 • a • a • b • b • b = 32 • 5 • a • a • b • b • b Write the variables without exponents.

6 What is the prime factorization of 48?
3  16 3  4  4 2  2  3  4 2  2  2  2  3

7 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.

8 4) Find the GCF of 42 and 60. = 2 • 3 • 7 60 = 2 • 2 • 3 • 5
= 2 •  • 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!

9 5) Find the GCF of 40a2b and 48ab4.
40a2b = 2 • 2 • 2 • 5 • a • a • b 48ab4 = 2 • 2 • 2 • 2 • 3 • a • b • b • b • b What do they have in common? Multiply the factors together. GCF = 8ab

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


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