factoring

FactoringFor use with section 1.2

Discovering Mathematics Book 1A

The Brandywine School District Mathematics Department

presents

What do we mean when we ask you to find the factors of a number?

Example: Find the factors of the number

Let’s look at how many ways we can arrange these six items into a rectangular array.

1 row of 6 or

6 rows of 1

1 and 6 are both factors of the number 6

Can we make any other rectangular

arrays with six objects?

2 rows of 3

Let’s look at how many ways we can arrange these six items into a rectangular array.

or3 rows of 2

2 and 3 are both factors of the number 6

Can we make any other rectangular

arrays with six objects?

The factors of the numberare 1, 2, 3, and 6

1 6 6 6 1 6 2 3 6 3 2 6

You try it! Find the factors of the number

1 8 8

8 1 8

2 4 8 4 2 8

The factors of the number 8are 1, 2, 4, and 8

Do all whole numbers have exactly four factors?Can you find a number with fewer than four factors?Can you find a number with more than four factors?

Can you find a number with fewer than four factors?

11

75

32

113

17

19and many

many more!

Can you find a number with more than four factors? 1

21 12 12 12 1 12 1 and 12 are factors of

122 6 12 6 2 12 2 and 6 are factors of

123 4 12 4 3 12 3 and 4 are factors of

12

12 has six factors: 1, 2, 3, 4, 6, and 12.

Numbers with exactly two factors

are called

Prime Numbers

11

75

32

113

17

19and many

many more!

Which of these numbers are PRIME

NUMBERS?

1Why isn’t PRIME?

1 1 1

The number 1 has only one factor!

Prime numbers have exactly two factors.

Whole numbers greater than one that aren’t prime numbers are called

Composite Numbers.

Writing whole numbers as the products of prime numbers!

Recall: The factors of the number 6 are 1, 2, 3, and 6

Only two of those factors are prime numbers.

The prime factorization of six is 2 x 3

You try it! Write the Prime Factorization of the following Composite Numbers:9 1

021

223 3 2 5 3 7 2 11

You try it! Write the Prime Factorization of the following Composite Numbers:8 1

216

242 4

Not Prime

2 2 2

2 62 2 3

2 82 2 4

2 2 2 2

2 122 2 6 2 2 2 3