1. Lesson 8-1 Monomials and Factoring
p. 471

2. Some definitions Remember that a factor is a number that is multiplied
The factors of a number are all the numbers that can be multiplied to get that number
One is a factor of every number
Every number is always a factor of itself
Ex. Find the factors of 12.
1,2,3,4,6,12
Prime Number – A whole number greater than one, whose only factors are one and itself.
Composite Number – A whole number greater than one that has more than two factors

3. Factors
Find the factors of each number, then write if it is prime or composite. 36
1,2,3,4,6,9,12,18, composite 23
1, prime

4. Prime Factorization
A number can be expressed as a product of its prime factors – this is prime factorization
To find the prime factorization of a number, you can use a factor tree.
Ex. Find the prime factorization of 90
To find the prime factorization of a negative number, start with negative 1
Ex. find the prime factorization of -140

5. Factored Form
A monomial is in factored form when it is expressed as a prime factorization and the variables are written out without exponents
Ex. Write each monomial in factored form 1. 2.

6. Problems to Try
Find the factors of each number and classify as prime or composite
Find the prime factorization of each number
Put each monomial in factored form

7. Greatest Common Factor (GCF)
To find the GCF of two numbers:
Find the prime factorization of the two numbers
Multiply the factors they have in common
Ex. Find the GCF of 48 and 60
Find the prime factorization of each number
Circle common factors
Multiply the common factors

8. Examples Find the GCF of: 1. 15 and 16
If the two number have no common factors then the GCF = 1.
The two numbers are called relatively prime. 2.

9. Example
The area of a rectangle is 28 square inches. If the length and width are both whole numbers, what is the maximum perimeter of the rectangle?
DRAW PICTURES TO SHOW YOU ALL POSSIBILITIES!
The greatest perimeter is 58 inches.

10. Problems to Try Find the GCF of: 1. 12 and 18 2.
3. Rene has crocheted 32 squares for an afghan. Each square is 1 foot square. She is not sure how she will arrange the squares but does know it will be rectangular and have a ribbon trim. What is the maximum amount of ribbon she might need to finish the afghan?