9.1 Factors and Greatest Common Factors

What you’ll learn:1. To find prime factorizations of

integers and monomials.2. To find the greatest common

factors of integers and monomials.

Vocabulary

1. Prime number – a whole number, greater than 1, whose only factors are one and itself.

2. Composite Number – a whole number, greater than 1, that has more than two factors

3. Prime Factorization – when a whole number is expressed as the product of factors that are all prime numbers.

4. Factored Form – a monomial is considered in this form when it is expressed as the product of prime numbers and variables with no variables with exponents greater than 1.

5. Greatest Common Factor (GCF) – the greatest number that is a factor of all the numbers. The GCF of two or more integers if the product of their common prime factors.The GCF of variables is the smallest exponent on common variables.

6. Relatively Prime – when two terms have a GCF of 1.

Find the factors of each number. Classify it as prime or composite.

1. 50

2. 130

Find the prime factorization of each integer. (Factor completely)

1. 80x³y⁵

2. -35a⁴b³c²

Find the GCF of each set of monomials.

1. 16xy², 24x⁴y³z

2. 15a²b, 35ab², 20abc

Homeworkp. 477

20-60 even72-77 all