4-2 Factors and Prime Factorization

Course 1

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpIdentify each number as prime or composite.

1. 19 2. 82

3. 57 4. 85

5. 101 6. 121

prime composite

composite

Course 1

4-2 Factors and Prime Factorization

composite

compositeprime

Problem of the Day

At the first train stop, 7 people disembarked. At the second stop, 8 people disembarked. At the fourth stop the last 6 people disembarked. If there were 28 people on the train before the first stop, how many people left at the third stop?

7 people left at the third stop

Course 1

4-2 Factors and Prime Factorization

Learn to write prime factorizations of composite numbers.

Course 1

4-2 Factors and Prime Factorization

Vocabulary

factorprime factorization

Insert Lesson Title Here

Course 1

4-2 Factors and Prime Factorization

Course 1

4-2 Factors and Prime Factorization

Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors.

2 3 6=

FactorsProduct

26 3÷ =

6 ÷2 = 36 is divisible by 3 and 2.

Course 1

4-2 Factors and Prime Factorization

When the pairs of factors begin to repeat, then you have found all of the factors of the number you are factoring.

Helpful Hint

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4-2 Factors and Prime Factorization

Additional Example 1A: Finding Factors

List all factors of 16.Begin listing factors in pairs.

16 = 1 • 1616 = 2 • 8

1 is a factor.2 is a factor.

16 = 4 • 43 is not a factor.4 is a factor.5 is not a factor.6 is not a factor.7 is not a factor.

16 = 8 • 2 8 and 2 have already been listed so stop here.

The factors of 16 are 1, 2, 4, 8, and 16.

1 2 44 168You can draw a diagram to illustrate the factor pairs.

Course 1

4-2 Factors and Prime Factorization

Additional Example 1B: Finding Factors

List all factors of 19.

Begin listing all factors in pairs.

19 = 1 • 19 19 is not divisible by any other whole number.

The factors of 19 are 1 and 19.

Course 1

4-2 Factors and Prime Factorization

Check It Out: Example 1A

List all factors of 12.

Begin listing factors in pairs.

12 = 1 • 1212 = 2 • 6

1 is a factor.2 is a factor.3 is a factor.4 and 3 have already been listed so stop here.

12 = 4 • 3

1 2 43 126

The factors of 12 are 1, 2, 3, 4, 6, and 12

12 = 3 • 4

You can draw a diagram to illustrate the factor pairs.

Course 1

4-2 Factors and Prime Factorization

Check It Out: Example 1B

List all factors of 11.

Begin listing all factors in pairs.

11 = 1 • 11 11 is not divisible by any other whole number.

The factors of 11 are 1 and 11.

Course 1

4-2 Factors and Prime Factorization

You can use factors to write a number in different ways.

Factorization of 12

2 • 61 • 12 3 • 4 3 • 2 • 2

The prime factorization of a number is the number written as the product of its prime factors.

Notice that these factors are all prime.

Course 1

4-2 Factors and Prime Factorization

You can use exponents to write prime factorizations. Remember that an exponent tells you how many times the base is a factor.

Helpful Hint

Course 1

4-2 Factors and Prime Factorization

Additional Example 2A: Writing Prime Factorizations

Method 1: Use a factor tree.

Choose any two factors of 24 to begin. Keep finding factors until each branch ends at a prime factor.

24

2 12•

6

2

2 •

3•

24

6 4•

3 2 2 2

24 = 2 • 2 • 2 • 3

24 = 3 • 2 • 2 • 2

The prime factorization of 24 is 2 • 2 • 2 • 3, or 23 • 3.

• •

Write the prime factorization of 24.

Course 1

4-2 Factors and Prime Factorization

Additional Example 2B: Writing Prime Factorizations

Method 2: Use a ladder diagram.

Choose a prime factor of 45 to begin. Keep dividing by prime factors until the quotient is 1.

3 45

3

1

15

55

45 = 3 • 3 • 5

5 45

3

1

9

3 3

45 = 5 • 3 • 3

The prime factorization of 45 is 3 • 3 • 5 or 32 • 5 .

Write the prime factorization of 45.

Course 1

4-2 Factors and Prime Factorization

In Example 2, notice that the prime factors may be written in a different order, but they are still the same factors. Except for changes in the order, there is only one way to write the prime factorization of a number.

Course 1

4-2 Factors and Prime Factorization

Check It Out: Example 2A

Write the prime factorization of 28.

Method 1: Use a factor tree.

Choose any two factors of 28 to begin. Keep finding factors until each branch ends at a prime factor.

28

2 14•

72 •

28

7 4•

2 2

28 = 2 • 2 • 7 28 = 7 • 2 • 2

The prime factorization of 28 is 2 • 2 • 7, or 22 • 7 .

•

Course 1

4-2 Factors and Prime Factorization

Check It Out: Example 2B

Write the prime factorization of 36.

Method 2: Use a ladder diagram.

Choose a prime factor of 36 to begin. Keep dividing by prime factors until the quotient is 1.

3 36

2

1

12

62

36 = 3 • 2 • 2 • 3

The prime factorization of 36 is 3 • 2 • 2 • 3, or 32 • 23.

3 36

3

1

12

2 4

36 = 3 • 3 • 2 • 2

33 2 2

Lesson Quiz

List all the factors of each number.

1. 22

2. 40

3. 51

1, 2, 4, 5, 8, 10, 20, 40

1, 2, 11, 22

Insert Lesson Title Here

1, 3, 17, 51

Course 1

4-2 Factors and Prime Factorization

Write the prime factorization of each number.

4. 32

5. 120

25

23 3 5