Prime numbers Composite numbers Neither prime nor composite How to know?

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Prime numbersComposite numbersNeither prime nor
compositeHow to know?
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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.

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Multiplication

• factor x factor product

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Prime Numbers

• To determine
• if a number is a prime number,
• place it in the product position.

X
Product Is this number a prime number?
Factor
Factor
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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.

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
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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...

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Prime Numbers
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

• 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.

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Prime Numbers

• A common misconception is
• that odd numbers
• are always prime numbers
• but, thats not true.

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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.

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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 isnt.

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Prime Numbers

• However, even numbers are never
• prime numbers
• with one exception
• the number 2.

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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
  (thats why no other even number is a prime
  number).

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Composite Numbers

• Numbers
• with more than two factors are called composite
  numbers. Numbers that arent prime numbers are
  composite numbers.

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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

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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.

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Only 0 and 1 are neither prime nor composite
numbers.

• All other whole numbers are either prime or
  composite numbers.

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Congratulations!

• Thats 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.

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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

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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