09-1+Factors+and+Greatest+Common+Factors

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.

Prime and Composite Numbers** ||  || and itself, is called a **Prime Number. Example: 2, 3, 5, 7, 11, 13, 17, 19 ** ||  || factors is called a **composite number. Example: 4, 6, 8, 9, 12, 14, 15, 16, 18… ** ||  ||
 * **Key Concept:
 * A whole number greater than 1, whose only factors are 1
 * A whole number, greater than 1, that has more than two

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.

Greatest Common Factor (GCF)** || prime factors common to the integers. || common factors when each monomial is in factored form. || the integers or monomials are said to be **relatively prime**. ||
 * **Key Concept
 * The GCF of two or more integers is the product of the
 * The GCF of two or more monomials is the product of their
 * If two or more integers or monomials have a GCF of 1, then

Worksheet 1

Worksheet 2

[|Factoring and GCF Help 2] [|Factoring Help]