Prime numbersComposite numbers

Neither prime nor compositeHow to know?

Prime and composite numbers are all about multiplication

Multiplication math vocabulary:

The two numbers being multiplied

together are each called factors.

The answer in a multiplication problem is

called the product.

Multiplication

factor x factor = product

Prime Numbers

To determine

if a number is a prime number,

place it in the product position.

ProductIs this number a prime number?

Factor X Factor =

Prime Numbers

1. Must have ONLY two possible, unique factors. (Both factors cannot be the same.)

2. One factor must be 1.

3. One factor must be a whole number, but not 0 or 1.

Factorsame number as the product,

but not 0 or 1.

X Factor

1

= Productsame number as

one of the factors,

but not 0 and not 1

Whole numbers

In case you forgot:

Whole numbers are the

the number 0, and the natural numbers which start at positive one—

{0, 1, 2, 3...}

Prime Numbers

3 is a prime number.1. There are ONLY two possible, unique factors.

(No other two numbers multiplied together have a product of 3 and both factors are different numbers.)

2. One factor is 1.

3. One factor is a whole number, but not 0 or 1.

3same number as the product,

but not 0 or 1.

X 1 = 3same number as

one of the factors,

but not 0 and not 1

Prime Numbers

A common misconception is

that odd numbers

are always prime numbersbut, that’s not true.

Prime Numbers

Some odd numbers,

like 9 have more than

two factors.9 x 1 = 9,

but so does 3 x 3.Consequently, 9 is not a prime number.

Prime Numbers

51 is tricky!

It is an odd number.

It looks like only 51 x 1 = 51, but17 x 3 = 51 too.

51 is not a prime number.

HINT: Divisibility rules and multiplication tables can help you discover that a number that seems like

a prime number really isn’t.

Prime Numbers

However, even numbers

are never

prime numbers with one exception—

the number 2.

Prime Numbers

2 is a prime number,because the only two factors

of 2

are 2 x 1 = 2. Every other even number has 2 as

a factor too (that’s why no other even number is a prime number).

Composite Numbers

Numbers with more than two factors

are called composite numbers. Numbers that aren’t prime numbers are composite numbers.

The special case of the number 1

The number 1 is

not a prime number and, it is not a composite number.Why? because, the number 1 only

has one factor, not two different factors.

1 x 1 = 1

The special case of the number 0.

Zero is another special number.

Zero can not be a prime number because,

every number is a factor of 0.

0 x 1 does equal 0, but

0 x anything at all = 0Zero is not a composite number either.

Only 0 and 1 are neither prime

nor composite numbers.

All other whole numbers are either prime or composite numbers.

Congratulations!

That’s how to tell a prime number from a composite number.

Remember, if in doubt; with big numbers, use divisibility rules.

With smaller products, use multiplication tables.

And all even numbers, except 2, are always composite.

Notes for teachers on texts correlation:

Correlates with Glencoe Mathematics (Florida Edition) texts:

Mathematics: Applications and Concepts Course 1: (red book)

Chapter 1 Lesson 3: Prime FactorsMathematics: Applications and Concepts Course 2:

(blue book) Chapter 5 Lesson 1: Prime FactorizationPre-Algebra: (green book) Chapter 4 Lesson 3: Prime FactorizationFor more information on my math class see http://

walsh.edublogs.org

Notes for teachers on design

This slide presentation was created using Microsoft Office PowerPoint 2003 part of Microsoft Office Standard Version for Students and Teachers.

Finally, thank you. I hope this is of help to your students. Taleese