Prime Numbers

Prime numbers Composite numbers Neither prime nor composite How 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.
Product Is this number a prime number ? Factor X Factor =

Prime Numbers
Must have ONLY two possible, unique factors. (Both factors cannot be the same.)
One factor must be 1.
One factor must be a whole number, but not 0 or 1 .
Factor same number as the product, but not 0 or 1. X Factor 1 = Product same 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 .
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 .
3 same number as the product, but not 0 or 1. X 1 = 3 same number as one of the factors, but not 0 and not 1

Prime Numbers
A common misconception is
that odd numbers
are always prime numbers
but, 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, but
17 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 = 0
Zero 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 Factors
Mathematics: Applications and Concepts Course 2: (blue book)
Chapter 5 Lesson 1: Prime Factorization
Pre-Algebra: (green book)
Chapter 4 Lesson 3: Prime Factorization
For 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

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Prime Numbers

by Taleese on Jun 17, 2008

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