Holt CA Course 1

3-1 Prime Factorization

Warm UpWarm Up

California StandardsCalifornia Standards

Lesson PresentationLesson Presentation

PreviewPreview

Holt CA Course 1

3-1 Prime Factorization

Warm UpWrite each number as a product of two whole numbers in as many ways as possible.

1. 6

2. 16

3. 17

4. 36

1 6, 2 3

1 16, 2 8, 4 4

1 17

1 36, 2 18, 3 12, 4 9, 6 6

Holt CA Course 1

3-1 Prime Factorization

Preparation for Preparation for Number Sense Number Sense (NS2.4)(NS2.4) - Determine the least - Determine the least common multiple and the greatest common multiple and the greatest common divisor of whole numbers;common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form for a fraction).

California Standards

Holt CA Course 1

3-1 Prime Factorization

Objective:Objective: You will learn You will learn how to find the prime how to find the prime factorization of composite factorization of composite numbers.numbers.

Holt CA Course 1

3-1 Prime Factorization

Vocabulary

prime numbercomposite numberprime factorization

Holt CA Course 1

3-1 Prime FactorizationA prime number is a whole number greater than 1 that has exactly two positive factors, 1 and itself. Three is a prime number because its only positive factors are 1 and 3.

A composite number is a whole number that has more than two positive factors. Six is a composite number because it has more than two positive factors—1, 2, 3, and 6. The number 1 has exactly one positive factor and is neither prime nor composite.

Holt CA Course 1

3-1 Prime Factorization

Tell whether each number is prime or composite.

Example 1: Identifying Prime and Composite Numbers

A. 11

11 is prime.

The positive factors of 11 are 1 and 11.

B. 16

16 is composite.

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

Holt CA Course 1

3-1 Prime Factorization

Tell whether each number is prime or composite.

Check It Out! Example 2

A. 14

14 is composite.

The positive factors of 14 are 1, 2, 7, and 14.

B. 7

7 is prime.

The positive factors of 7 are 1 and 7.

Holt CA Course 1

3-1 Prime FactorizationA composite number can be written as the product of its prime factors. This is called the prime factorization of the number.

You can use a factor tree to find the prime factors of a composite number.

You can also use the “Stairs Method” to find the prime factors of a composite number.

Holt CA Course 1

3-1 Prime Factorization

You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor.

Writing Math

Holt CA Course 1

3-1 Prime Factorization

Write the prime factorization of the number 2424.

Example 3: Using a Factor Tree to Find Prime Factorization

24

8 3

4 2

2 2

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

Holt CA Course 1

3-1 Prime FactorizationCheck It Out! Example 4

Write the prime factorization of the number 9090.

90

45 2

9 5

3 3

The prime factorization of 90 is 3 3 5 2, or 2 32 5.

Holt CA Course 1

3-1 Prime Factorization

Write the prime factorization of the number 150150.

Example 5: Using a Factor Tree to Find Prime Factorization

150

30 5

10 3

2 5

The prime factorization of 150 is 2 3 5 5, or 2 3 52.

Holt CA Course 1

3-1 Prime FactorizationCheck It Out! Example 6

Write the prime factorization of the number 225225.

225

45 5

9 5

3 3

The prime factorization of 225 is 3 3 5 5, or 32 52.

Holt CA Course 1

3-1 Prime Factorization

You can also use the “Stairs Method” to find the prime factorization of a number. At each step, divide by the smallest possible prime number. Continue dividing until the quotient is 1.

Holt CA Course 1

3-1 Prime Factorization

Write the prime factorization of the number 476476.

Example 7: Using the “Stairs Method” to Find Prime Factorization

476238119

171

22

717

The prime factorization of 476 is 2 2 7 17, or 22 7 17.

Holt CA Course 1

3-1 Prime Factorization

There is only one prime factorization for any given composite number. Example 2A began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result.

476238119

171

22

717

4766834

171

72

217

The prime factorizations are 2 2 7 17 and7 2 2 17, which are the same as 17 2 2 7.

Holt CA Course 1

3-1 Prime Factorization

Write the prime factorization of the number 275275.

Example 8: Using the “Stairs Method” to Find Prime Factorization

27555111

5511

The prime factorization of 275 is 5 5 11, or 52 11.

Holt CA Course 1

3-1 Prime FactorizationCheck It Out! Example 9

Write the prime factorization of the number 324324.

324162

8127

1

22

33

The prime factorization of 324 is 2 2 3 3 3 3, or 22 34.

9333

Holt CA Course 1

3-1 Prime Factorization

Check It Out! Example 10

Write the prime factorization of the number 325325.

32565131

5513

The prime factorization of 325 is 5 5 13, or 52 13.

Holt CA Course 1

3-1 Prime Factorization

Home Home

LearningLearning

On-Line On-Line TutoringTutoring

Factor Factor TreesTrees

Prime Prime WarsWars

Factor Factor GameGame

Holt CA Course 1

3-1 Prime Factorization

Lesson Quiz

Tell whether each number is prime or composite.

1. 23 2. 39 3. 27

compositeprime composite

Write the prime factorization of each number.

4. 27 5. 36

6. 28 7. 132

8. 52 9. 108

22 3233

22 7 22 3 11

22 13 22 33