1. Section 5-1 Factoring Numbers

2. Factor
When two or more numbers are multiplied, each of the numbers is a factor of the product.
Example:
48 = 6 ● 8
6 and 8 are factors of 48

3. Factor Set The set of factors for a given number. Example:
List all the positive pairs of factors of 48.
{1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

4. Prime
An integer greater than 1 that has no positive integral factor other than itself and 1.
Example: 2, 3, 5, 7, 11, 13, 17,…
0 and 1 are neither prime nor composite!
2 is the only even prime number!

5. Prime Factorization
Expressing a positive integer as a product of primes
Example: Write the prime factorization of 48. 48
48 = 24 ● 3 6 8 3 2 4 2 2 2

6. Common Factor A factor of two or more integers Example:
5 is a common factor of 15 and 25
3 is a common factor of 6 and 18

7. Greatest Common Factor
The common factor with the greatest coefficient and the greatest degree in each variable.
Example:
Find the GCF of 66 and 90.