Perfect Numbers

Designed by The CountessesJill, Kathy, Bev, Karen & Sarah

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.

Definition

A Perfect Number is a number that has

equal factors.

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.

More Examples of Perfect Numbers

8 = 2x2x2 1000 = 10x10x10

125 = 5x5x5

The numbers in black are perfect cubes because they have 3 equal factors.

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

No This is a Perfect Square.

This number has two equal factors.

Return

Yes This is a Perfect Cube.

This number has three equal factors.

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

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.

Remember !!!

A Perfect Number is a number that has

equal factors.

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.

Which two fractions are perfect?

9/25 16/21

1/36 23

25

8/25

Good Job !!!

This number is

Perfect.

Return

Sorry

Review the Rules

This number is not

Perfect.

Back to the quiz

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.

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)

Which two are perfect?

-25 -27

-16-1000

Good Job !!!

This number is

Perfect.

Return

Sorry

Review the Rules

This number is not

Perfect.

Back to the quiz

Remember !!

Perfect cubes can be negative.

Perfect squares cannot be negative.

A Perfect Number is a number that has equal factors.

Final Quiz

End

Click on numbers that are perfect. ( There are 6.)

100

49/81

1711

- 9

1/7- 8/27

Good job!!

Find More

This number is Perfect!!!

Sorry

TRY AGAIN

This number is

Not Perfect!!