Download Section 5.1 Factoring Numbers

Section 5.1
Factoring 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
3
48=24 ● 3
8
2 4
2
2
2
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.