1. Finding GCF
SOL A.2c

2. Prime and Composite
A prime number is a number that has exactly two factors, one and itself.
A composite number is a number greater than one that is not prime. It will have more than 2 factors.
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. A monomial is in factored form when it is expressed as the product of prime numbers and variables and no variable has an exponent greater than 1.

6. Example 1: 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.

7. Example 2: Find the prime factorization of -68pq2
-68pq2 = -1 • 2 • 34 • p • q • q = -1 • 2 • 2 • 17 • p • q • q = -1 • 22 • 17 • p • q • q Write the variables without exponents.

8. The Greatest Common Factor (GCF) of 2 or more integers is the product of the prime factors common to the integers. The GCF is the largest number that can divide into all of the numbers.
The GCF of two or more monomials is the product of their common factors when each monomial is in factored form.

9. Finding the GCF
1. Factor each number 2. Circle the common prime factors, if any 3. Find the product of the common prime factors (circled numbers)

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

11. Example 4: 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 prime factors do they have in common? Multiply the factors together. GCF = 8ab

12. Example 5: Find the GCF of 15 and 16.
15: 3 • 5
16: 2 • 2 • 2 • 2
There are no common factors, so the GCF of 15 and 16 is one.
This means that 15 and 16 are relatively prime.