Perfect Numbers

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Perfect Numbers
Designed by Karen Wingart kwingart_at_aol.com
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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.

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Definition

• A Perfect Number is a number that has
• equal factors.

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Examples of perfect numbers

• 4 2x2 25 5x5 1 1x1
• 64 8x8 81 9x9 36 6x6

The numbers in black are all perfect squares
because they have 2 equal factors.
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More Examples of Perfect Numbers
8 2x2x2 1000 10x10x10 125 5x5x5
The numbers in black are perfect cubes because
they have 3 equal factors.
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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.
27
49
144
125
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No This is a Perfect Square.
This number has two equal factors.
Return
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Yes This is a Perfect Cube.
This number has three equal factors.
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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

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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.
Remember Numbers can be perfect squares or
perfect cubes.
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Remember !!!
A Perfect Number is a number that has equal
factors.
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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.
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Which two fractions are perfect?
9/25
16/21
8/25
23 25
1/36
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Good Job !!!
This number is Perfect.
Return
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Sorry
This number is not Perfect.
Review the Rules
Back to the quiz
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Remember !!
A Perfect Number is a number that has equal
factors.
Note If both the numerator and denominator are
perfect squares or if both are perfect cubes,
then the fraction is perfect.
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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)
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Which two are perfect?
-27
-25
-16
-1000
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Good Job !!!
This number is Perfect.
Return
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Sorry
This number is not Perfect.
Review the Rules
Back to the quiz
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Remember !!
A Perfect Number is a number that has equal
factors.
Perfect cubes can be negative. Perfect squares
cannot be negative.
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Final Quiz
Click on numbers that are perfect. ( There are 6.)
17
11
49/81
- 9
400
1/7
- 8/27
100
End
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Good job!!
This number is Perfect!!!
Find More
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Sorry
This number is Not Perfect!!
TRY AGAIN