8

Click here to load reader

ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

Embed Size (px)

Citation preview

Page 1: ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

ALGEBRA READINESS

LESSON 4-2

Warm Up Lesson 4-2 Warm Up

Page 2: ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

ALGEBRA READINESS

LESSON 4-2

Warm Up

Lesson 4-1 Warm Up

Page 3: ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

ALGEBRA READINESS

“Greatest Common Divisor” (4-2)

What is a “common divisor”?

What is the “greatest common divisor?

Common Divisor: a divisor (factor) that two or more numbers shareExample: What are the common divisors of 18 and 24?•Divisors of 18: 1, 2, 3, 6, 9, 18•Divisors of 24: 1, 2, 3, 4, 6, 8, 12, 24The common divisors of 18 and 24 are 1, 2, 3, and 6.

Greatest Common Divisor (also known as the GCF): the largest common divisor shared by two or more numbersExample: What is the GCF of 20 and 42?•Divisors of 20: 1, 2, 4, 5, 10, 20•Divisors of 12: 1, 2, 3 , 4, 6, 12The greatest common divisors or GCF of 20 and 12 is 4.

Page 4: ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

ALGEBRA READINESS

List the divisors to find the GCD of 48 and 64.

List the divisors of 48 and the divisors of 64. Then circle thecommon divisors.

Divisors of 48: 1 , 2 , 3, 4 , 6, 8 , 12, 16 , 24, 48

Divisors of 64: 1 , 2 , 4 , 8 , 16 , 32, 64

The greatest common divisor (GCD) is 16.

The common divisors are 1, 2, 4, 8, and 16.

Greatest Common DivisorLESSON 4-2

Additional Examples

Page 5: ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

ALGEBRA READINESS

“Greatest Common Divisor” (4-2)

How can you use prime factorization to find the GCD?

To use prime factorization to find the GCD:

1.Find the prime factorization of each number.

2.Multiply the common factors together.

Example: Find the GCF of 18, 27, and 36.

Factor Trees for 18, 27, and 36

1. Write the prime factorization for each number.

2. Multiply common factors.

The GCD of 18, 27, and 36 is 9.

Page 6: ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

ALGEBRA READINESS

Two ribbons have lengths of 28 cm and 42 cm. You cut

both ribbons into pieces of equal length with nothing left over.

What is the greatest possible length of the pieces?

Make a factor tree to find theprime factorization of eachnumber.

2 14

2 7

28

7 2

14 3

42

To find the greatest possible lengths of the pieces, find theGCD of 28 and 42.

Greatest Common DivisorLESSON 4-2

Additional Examples

Page 7: ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

ALGEBRA READINESS

The GCD of 28 and 42 is 14, so the greatest possible length of the pieces is 14 cm.

2 7 = 14 2. Multiply the common factors.

Identify common factors.

1. Write the prime factorization for each number. 28 = 2 2 742 = 2 3 7

(Continued)

Greatest Common DivisorLESSON 4-2

Additional Examples

Page 8: ALGEBRA READINESS LESSON 4-2 Warm Up Lesson 4-2 Warm Up

ALGEBRA READINESS

Find the GCD of each set of numbers.

1. 60, 80 2. 24, 57

3. 36, 48 4. 115, 70, 200

20 3

12 5

Greatest Common DivisorLESSON 4-2

Lesson Quiz