Download Alg1 Notes 7.1.notebook

Alg1 Notes 7.1.notebook
February 15, 2013
7­1 Factors and Greatest Common Factors
Skills we need
Tell whether the second number is a factor of the first number 1. 50, 6 2. 105, 7
3. List the factors of 28.
Tell whether each number is prime or composite. If the number is composite, write it as the product of two numbers.
Warm­up Answers
Alg1 Notes 7.1.notebook
February 15, 2013
7­1 Factors and Greatest Common Factors
1. Write the prime factorization of numbers.
2. Find the GCF of monomials This is the first step to factoring
I. Writing Prime Factorizations
The whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors and when all those factors are prime it is called prime factorization.
1. Write the prime factorization of 98. Alg1 Notes 7.1.notebook
February 15, 2013
2. Write the prime factorization of each number.
A. 40
B. 33
C. 49
II. Finding the GCF of Numbers
3. Find the GCF of each pair of 100 and 60.
Method 2 Prime factorization
prime factors of 100: 2 2 5 5
prime factors of 60: 2 2 3 5
The GCF of 100 and 60 is 2 2 5 = 20
D. 19
Alg1 Notes 7.1.notebook
February 15, 2013
4. Find the GCF of each pair of numbers.
A. 12 and 16
B. 35 and 70
C. 22 and 13
III. Finding GCF of Monomials
You can also find the GCF of monomials that include variables. To find the GCF of monomials, write the prime factorization of each coefficient and write all powers of variables as products. Then find the product of the common factors.
5. Find the GCF of each pair of monomials.
15x3 and 9x2
The GCF of 15x3 and 9x2 is 3x2.
Alg1 Notes 7.1.notebook
February 15, 2013
6. Find the GCF of each pair of monomials.
A. 8x2 and 7y3
B. 18g2 and 27g3
C. 16a6 and 9b
IV. Application
7. A cafeteria has 18 chocolate­milk cartons and 24 regular­milk cartons. The cook wants to arrange the cartons with the same number of cartons in each row. Chocolate and regular milk will not be in the same row. How many rows will there be if the cook puts the greatest possible number of cartons in each row? GCF of 18 & 24 = The greatest possible number of milk cartons in each row is 6. Find the number of rows of each type of milk when the cook puts the greatest number of cartons in each row. When the greatest possible number of types of milk is in each row, there are 7 rows in total.
Alg1 Notes 7.1.notebook
February 15, 2013
7.1 p.459 #3 ­ 12 (x3), 13 ­ 16, 20, 25, 30, 33, 38, 41, 47, 51, 60, 61