2. Perfect Numbers Designed by The Countesses Jill, Kathy, Bev, Karen & Sarah

3. Perfect Numbers In this presentation you will learn what perfect numbers are and how to identify them. You will look at whole numbers, fractions, and negative numbers.

4. Definition A Perfect Number is a number that has equal factors.factors

5. Examples of perfect numbers 4 = 2x225 = 5x51= 1x1 64 = 8x881 = 9x936 = 6x6 The numbers in black are all perfect squares because they have 2 equal factors.

6. More Examples of Perfect Numbers 8 = 2x2x21000 = 10x10x10 125 = 5x5x5 The numbers in black are perfect cubes because they have 3 equal factors.

7. TRY THESE !!! Three of the following numbers are perfect squares. Two of the following numbers are perfect cubes? Find both of the perfect cubes before you go on. 49 144 27 125

8. No This is a Perfect Square. This number has two equal factors. Return

9. Yes This is a Perfect Cube. This number has three equal factors.

10. Factor A factor is a number that divides into another with no remainder.  2 is a factor of 6 because:  2 divides into 6 three times with no remainder  2 is not a factor of 7 because:  2 divides into 7 three times with a remainder of one

11. Special numbers In addition to whole numbers, you will look at fractions and negative numbers. The Rule for perfect numbers still applies to fractions and negative numbers. Rule Remember – Numbers can be perfect squares or perfect cubes.

12. Remember !!! A Perfect Number is a number that has equal factors.

13. Fractions that are perfect numbers If both the numerator and denominator are perfect squares or if both are perfect cubes, then the fraction is perfect. ¼ = ½ x ½ 9/25 = 3/5 x 3/5 8/27 = 2/3 x 2/3 x 2/3 3/25 is not perfect because 3 is not perfect. 4/27 is not perfect because 4 is a perfect square and 27 is a perfect cube.

14. Which two fractions are perfect? 9/25 16/21 1/36 23 25 8/25

15. Good Job !!! This number is Perfect. Return

16. Sorry Review the Rules This number is not Perfect. Back to the quiz

17. Remember !! Note: If both the numerator and denominator are perfect squares or if both are perfect cubes, then the fraction is perfect. A Perfect Number is a number that has equal factors.

18. Negative Numbers that are Perfect Perfect cubes can be negative. -8 is perfect because -8 = -2 x -2 x -2 Perfect squares cannot be negative. -4 is not perfect because -4 does not have two equal factors. (-2 x -2  -4 and 2 x 2  -4)

19. Which two are perfect? -25 -27 -16 -1000

20. Good Job !!! This number is Perfect. Return

21. Sorry Review the Rules This number is not Perfect. Back to the quiz

22. Remember !! Perfect cubes can be negative. Perfect squares cannot be negative. A Perfect Number is a number that has equal factors.

23. Final Quiz End Click on numbers that are perfect. ( There are 6.) 100 49/81 17 11 - 9 1/7 - 8/27

24. Good job!! Find More This number is Perfect!!!

25. Sorry TRY AGAIN This number is Not Perfect!!