Factors and Prime Factors

5.2

What Will We Accomplish?

• After reviewing the characteristics of prime and composite numbers . . . .

We will write the prime factorization of composite numbers.

We will look at this skill in three ways. The “Think Box” method will be the most useful in future math classes.

Prime or Composite Review

• It is helpful to identify a number as prime or composite when trying to simplify a value.

• Prime numbers have only two factors: Itself and the number 1.

• The number “1” is neither prime nor composite. It has only one factor.

• The number 2 is the only even number that is prime.

Factors are multiplication “facts.”

Factors: whole numbers that are multiplied together to form a product

Prime factorization: writing a product using ONLY PRIME NUMBERS as a multiplication problem.

8 = 2 x 2 x 2 = 23

Prime FactorizationMethod 1: Factor Trees

Start with the composite number, and break it into two of its factors.

48 48

6 X 8 12 X 4

2 X 3 4 X 2

2 X 2

00000

The prime factors are 2 2 2 3 2= 2∙ ∙ ∙ ∙ 4 3∙

2 x 26 X 2

3 X 2

0 0000

Prime Factorization: Factor Tree Practice

Start with the composite number, and break it into two of its factors.

30 50

3 x 10 5 x 10

3 x 2 x 5

2 x 3 x 5

2 x 5 x 5 = 2 x 52

000

003 x 3

5 x 2

9 x 10

0 0000

90

2 x 5

2 x 5 x 3 x 3 = 2 x 32 x 5

Remember Our Objective!

• We are rewriting composite numbers as prime factors.

• This means we are writing multiplication problems that ONLY have prime factors in them!

Prime Factorization: Method 2Division Ladders

When using a division ladder, use only primes to divide.

482

242

122

62

3

These are your prime factors:2 x 2 x 2 x 2 x 3

303

1025

The prime factors are 2 x 3 x 5

Add this to your notes.

Prime Factorization: Division Ladder Practice

Remember, use only primes to divide.

1002

502

2555

2 x 2 x 5 x 5 = 22 x 52

2505505

10

5 x 5 x 5 x 2 = 2 x 53

52

Prime Factorization: Method 3Think Box Primes

This is a new method. This is the method that will help you with therest of the chapter and into next year. It is shown in a different form in your text.

48 =

Make a “think box” to organize your thoughts.List two factors that = 48.

6 x 8 =

Take one factor at a time and break it into prime factors.

3 x 2

Remembering that 8 = 2 x 2 x 2 will save you a tremendous amount of time!

x 2 x 2 x 2

90 = 9 x 10 = 3 x 3 x 2 x 5

2 x 32 x 5

120 = 12 x 10 = 2 x 2 x 3 x 2 x 5 23 x 3 x 5

66 = 6 x 11 = 2 x 3 x 11

88 =

Remember the 8!!!!

8 x 11 = 2 x 2 x 2 x 11 23 x 11=

Think Box Practice

36 = 6 x 6 = 2 x 3 x 2 x 3 22 x 32

45 = 5 x 9 = 5 x 3 x 3 5 x 32

1500 = 15 x 100 = 3 x 5 3 x 22 x 53

2 x 5 x 2 x 5

x 2 x 5 x 2 x 5

Have We Met Our Objective?

• Did we write composite numbers in the form of prime factorizations?

• Did you find one method you preferred over the others?

• Remember, you do not always have to use one method. You can use a method that works best for a specific problem.

• However….which one will be the most help in future math classes?

Think in terms of primes.

Speed limits? 7 x 2 x 5

Ages? 2 x 2 x 3

Grades? 2 x 5 x 2 x 5

PRIMES