Section 5.1Factoring Numbers

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

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}

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!

Prime Factorization

• Expressing a positive integer as a product of primes– Example: Write the prime factorization of 48.

48

6 8

3 2 4 2

2 2

48=24 ● 3

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

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.