Prime Numbers

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Prime and composite numbers; special case of 1 and 0

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Prime Numbers

  1. 1. Prime numbers Composite numbers Neither prime nor composite How to know?
  2. 2. Prime and composite numbers are all about multiplication <ul><li>Multiplication math vocabulary: </li></ul><ul><li>The two numbers being multiplied together are each called factors . </li></ul><ul><li>The answer in a multiplication problem is called the product . </li></ul>
  3. 3. Multiplication <ul><li>factor x factor = product </li></ul>
  4. 4. Prime Numbers <ul><li>To determine </li></ul><ul><li>if a number is a prime number , </li></ul><ul><li>place it in the product position. </li></ul>Product Is this number a prime number ? Factor X Factor =
  5. 5. Prime Numbers <ul><li>Must have ONLY two possible, unique factors. (Both factors cannot be the same.) </li></ul><ul><li>One factor must be 1. </li></ul><ul><li>One factor must be a whole number, but not 0 or 1 . </li></ul>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
  6. 6. Whole numbers <ul><li>In case you forgot: </li></ul><ul><li>Whole numbers are the </li></ul><ul><li>the number 0, and the natural numbers which start at positive one— { 0, 1, 2, 3... } </li></ul>
  7. 7. Prime Numbers <ul><li>3 is a prime number . </li></ul><ul><li>There are ONLY two possible, unique factors. </li></ul><ul><li>(No other two numbers multiplied together have a product of 3 and both factors are different numbers.) </li></ul><ul><li>2. One factor is 1. </li></ul><ul><li>3. One factor is a whole number, but not 0 or 1 . </li></ul>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
  8. 8. Prime Numbers <ul><li>A common misconception is </li></ul><ul><li>that odd numbers </li></ul><ul><li>are always prime numbers </li></ul><ul><li>but, that’s not true. </li></ul>
  9. 9. Prime Numbers <ul><li>Some odd numbers , </li></ul><ul><li>like 9 have more than </li></ul><ul><li>two factors . </li></ul><ul><li>9 x 1 = 9 , </li></ul><ul><li>but so does 3 x 3 . </li></ul><ul><li>Consequently, 9 is not a prime number. </li></ul>
  10. 10. Prime Numbers <ul><li>51 is tricky! </li></ul><ul><li>It is an odd number. </li></ul><ul><li>It looks like only 51 x 1 = 51, but </li></ul><ul><li>17 x 3 = 51 too . </li></ul><ul><li>51 is not a prime number . </li></ul><ul><li>HINT : Divisibility rules and multiplication tables can help you discover that a number that seems like a prime number really isn’t. </li></ul>
  11. 11. Prime Numbers <ul><li>However , even numbers are never </li></ul><ul><li>prime numbers </li></ul><ul><li>with one exception— </li></ul><ul><li>the number 2 . </li></ul>
  12. 12. Prime Numbers <ul><li>2 is a prime number , </li></ul><ul><li>because the only two factors </li></ul><ul><li>of 2 </li></ul><ul><li>are 2 x 1 = 2. </li></ul><ul><li>Every other even number has 2 as a factor too (that’s why no other even number is a prime number). </li></ul>
  13. 13. Composite Numbers <ul><li>Numbers </li></ul><ul><li>with more than two factors are called composite numbers . Numbers that aren’t prime numbers are composite numbers. </li></ul>
  14. 14. The special case of the number 1 <ul><li>The number 1 is </li></ul><ul><li>not a prime number and, </li></ul><ul><li>it is not a composite number. </li></ul><ul><li>Why ? because, the number 1 only has one factor , not two different factors . </li></ul><ul><li>1 x 1 = 1 </li></ul>
  15. 15. The special case of the number 0. <ul><li>Zero is another special number. </li></ul><ul><li>Zero can not be a prime number because, </li></ul><ul><li>every number is a factor of 0 . </li></ul><ul><li>0 x 1 does equal 0, but </li></ul><ul><li>0 x anything at all = 0 </li></ul><ul><li>Zero is not a composite number either. </li></ul>
  16. 16. Only 0 and 1 are neither prime nor composite numbers. <ul><li>All other whole numbers are either prime or composite numbers. </li></ul>
  17. 17. Congratulations! <ul><li>That’s how to tell a prime number from a composite number. </li></ul><ul><li>Remember, if in doubt; with big numbers, use divisibility rules. </li></ul><ul><li>With smaller products, use multiplication tables. </li></ul><ul><li>And all even numbers, except 2, are always composite. </li></ul>
  18. 18. Notes for teachers on texts correlation: <ul><li>Correlates with Glencoe Mathematics (Florida Edition) texts: </li></ul><ul><li>Mathematics: Applications and Concepts Course 1: (red book) </li></ul><ul><li>Chapter 1 Lesson 3: Prime Factors </li></ul><ul><li>Mathematics: Applications and Concepts Course 2: (blue book) </li></ul><ul><li>Chapter 5 Lesson 1: Prime Factorization </li></ul><ul><li>Pre-Algebra: (green book) </li></ul><ul><li>Chapter 4 Lesson 3: Prime Factorization </li></ul><ul><li>For more information on my math class see http:// walsh.edublogs.org </li></ul>
  19. 19. Notes for teachers on design <ul><li>This slide presentation was created using Microsoft Office PowerPoint 2003 part of Microsoft Office Standard Version for Students and Teachers. </li></ul><ul><li>Finally, thank you. I hope this is of help to your students. Taleese </li></ul>

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