9-1 Factors and Greatest Common Factors

When two or more numbers are multiplied, each number is a factor of the product. Some numbers like 18, can be expressed as the product of different pairs of whole numbers. This can be shown geometrically. Consider all of the possible rectangles with whole number dimensions that have areas of 18 square units.

Key Concept:
Prime and Composite Numbers

A whole number greater than 1, whose only factors are 1
and itself, is called a Prime Number.
Example: 2, 3, 5, 7, 11, 13, 17, 19

A whole number, greater than 1, that has more than two
factors is called a composite number.
Example: 4, 6, 8, 9, 12, 14, 15, 16, 18…

When a whole number is expressed as the product of factors that are all prime number, the expression is called the prime factorization of the number.

A negative integer is factored completely when it is expressed as the product of -1 and prime numbers.

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.

Key Concept
Greatest Common Factor (GCF)

The GCF of two or more integers is the product of the
prime factors common to the integers.
The GCF of two or more monomials is the product of their
common factors when each monomial is in factored form.
If two or more integers or monomials have a GCF of 1, then
the integers or monomials are said to be relatively prime.

Worksheet 1

Worksheet 2

Factoring and GCF Help 2
Factoring Help