Perfect Numbers Designed by The Countesses Jill Kathy

Perfect Numbers Designed by The Countesses Jill, 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 = 2 x 2 25 = 5 x 5 1= 1 x 1 64 = 8 x 8 81 = 9 x 9 36 = 6 x 6 The numbers in black are all perfect squares because they have 2 equal factors.

More Examples of Perfect Numbers 8 = 2 x 2 x 2 1000 = 10 x 10 125 = 5 x 5 x 5 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. 27 125 144 49

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 n A factor is a number that divides into another with no remainder. q 2 is a factor of 6 because: § q 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=½x½ 9/25 = 3/5 x 3/5 8/27 = 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 23 1/36 25 8/25

Good Job !!! This number is Perfect. Return

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

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.

Negative Numbers that are Perfect cubes can be negative. -8 is perfect because -8 = -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 -1000 -27 -16

Good Job !!! This number is Perfect. Return

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

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

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

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

Sorry This number is Not Perfect!! TRY AGAIN