Divisivility Rules 1.ppt

7/31/2019 Divisivility Rules 1.ppt

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Easily test if one number can be

evenly divided by another


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Divisible By"Divisible By" means "when you divide one number by another the

result is awhole number"

Examples:

14 is divisible by 7, because 14 7 = 2 exactly

But 15 is not divisible by 7, because 15 7 = 2 1/7

(i.e., the result is not a whole number)

"Divisible by" and "can be evenly divided by"

mean the same thing


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The Divisibility Rules

These rules let you test if one number is divisibleby another, without having to do too muchcalculation!

A number is

divisible by:==========

If:

===================Example:

===================

2 The last digit is even(0,2,4,6,8)128

129

yes

no

3 The sum of the digits isdivisible by 3

381

(3+8+1=12, and 123 = 4)

217

(2+1+7=10, and 103 = 3 1/3)

yes

no


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If:

===================

A number isdivisible by:==========

Example:

===================

4 The last 2 digits aredivisible by 4

1 3 1 2 (124=3)7 0 1 9

yes

no

5 The last digit is 0 or 5 175809 yesno

6 The number is divisible

by both 2and

3

114

( 1+1+4=6 )

( 63 = 2 )

yes

it is even

it is even

308

(3+0+8=11 & 113 =3 2/3)

it is even no


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If:

===================


Example:

===================

7 If you double the last digitand subtract it from therest of the number and theanswer is:

0 divisible by 7or

672

Double 2 is 4

67 - 4 = 63

63 7 = 9

yes

905

Double 5 is 10

90 10 = 80

80 7 = 11 3/7

no


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If:

===================


Example:

===================

8 The last three digits aredivisible by 8

yes

no

109816

816 8 = 102

216302

302 8 = 37 3/4

9 The sum of the digits isdivisible by 9

yes1629

1+6+2+9=18

1+8=9

2013 no

2+0+1+3=6


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If:

===================


Example:

===================

10 The number ends in 0 yesno

11 If you sum every seconddigit and then subtract allother digits and the answeris:

yes

no

220

221

0or

divisible by 11

1364

((3+4) - (1+6) = 0)

3729

((7+9) - (3+2) = 11)

yes

25176

((5+7) - (2+1+6) =3)


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If:

===================


Example:

===================

10 The number ends in 0 yesno

11 If you sum every seconddigit and then subtract allother digits and the answeris:

yes

no

220

221

0or

divisible by 11

1364

((3+4) - (1+6) = 0)

3729

((7+9) - (3+2) = 11)

yes

25176

((5+7) - (2+1+6) =3)


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If:

===================


Example:

===================

yes12

no

The number isdivisible by both 3and4

648

6+4+8=18

183=6

484=12

916

9+1+6=16

163= 5 1/3


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There are lots more!

Not only are there divisibilitytests for larger numbers, but

there are more tests for thenumbers we have shown.


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Factors Can Be Useful

Factors are the numbers you multiply to get another number:

This can be useful, because:

When a number is divisible by another number ...

... then it is also divisible by each of the factors of that number.

Example:

If a number is divisible by 6, it is alsodivisible by 2 and 3

If a number is divisible by 12, it is also divisibleby 2, 3, 4 and 6


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Divisivility Rules 1.ppt

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