Divisibility

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What is Divisibility? Divisibility means that after dividing, there will be No remainder.

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356,821Can you tell by just looking at this number if it is divisible by 2?

by 5? by 10? by 3 ?by 9?By 6?

The divisibility rules can help

YOU!

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Divisibility Rules help you learnhelp you learn

shortcuts to tell when to tell when a number can be a number can be

divided by another divided by another number with number with

NO REMAINDER..

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Dividing By 1All numbers are divisible by 1

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Now You TryAre these numbers divisible by 1?

a) 578b) 1201c) 465

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Dividing by 2All even numbers are divisible by 2

Even numbers are numbers that

end with either 2, 4, 6, 8, or 0

18 ÷ 2 = 9 22 ÷ 2 = 11

Notice that both of these numbers are even.

21 ÷ 2 = 10 R1 NOT EVEN

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Now You TryAre these numbers divisible by 2?

a) 458b) 1279c) 759

Not an even number

Not an even number

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Dividing by 3 A number is divisible by 3 if the sum of the digits is divisible by 3.

Is the number 135 divisible by 3?

Add the digits: 1 + 3 + 5 = 9

Yes, 135 is divisible by 3 because the sum of the digits is divisible by 3.

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Now You TryAre these numbers divisible by 3?

a) 639Sum of 6+3+9 =18

b) 56 Sum of 5+6 =11 NO

c) 738Sum of 7+3+8 =18

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Dividing by 4If the last 2 digits together are divisible

by 4

or take your number, divide it by 2. Then divide that answer by 2, and if you get an EVEN NUMBER then it is divisible by 4

2)360180 EVEN

2)180 90 EVENExample

360

4)84 21

Example

384

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Now You TryAre these numbers divisible by 4?

a) 584

b) 261

4)84 21

4)61 15 r1 NO

Take the last 2 digits and divide by 4

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Dividing by 5If the number ends in 5 or 0

25 ÷ 5 = 5 23 ÷ 5 = 4 R3 NO

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Now You TryAre these numbers divisible by 5?

a) 554

b) 6890

c) 345

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Dividing by 6If the number is divisible by 2,

AND . . .

If the number is divisible by 3

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Now You TryAre these numbers divisible by 6?

a) 897

b) 258

c) 630

No it is not EVEN

EVEN, Sum of 2+5+8 =15 EVEN, Sum of 6+3+0 =9

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Dividing by 7

There is no special rule to help you know if a number is divisible by 7…

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Now You TryAre these numbers divisible by 7?

a) 500b) 49c) 2100

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Dividing by 8 If the last three digits are divisible

by 8 If the number is divisible by 2, then by 2 again, and then by 2 again

So what type of number does it have to be?

3 2 8

2 2 2 = 8

A number that has been cubed.

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Now You TryAre these numbers divisible by 8?

a) 568 2)568 284 Even

2)284142 Even

2)142 71

b) 396 2)396 198 Even

2)19899 Odd

NO

Take the last 3 digits and divide by 2, then divide by 2,

then divide by 2

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Dividing by 9Similar to dividing by 3

Add up digits

If that number is divisible by 9 then your number is divisible by 9

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Dividing by 9

If that number is divisible by 9, then the original number is

If your sum is still a big number, continue to add the digits

Add up the digits of the number 27

Is 27 divisible by 9?

2 + 7 = 9

For example, take the number 924,561

9 + 2 + 4 + 6 +5 + 1 =

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Now You TryAre these numbers divisible by 9?

a) 578

b) 399

c) 144

Sum of 5+7+8 =20 NO Sum of 3+9+9 =21 NO Sum of 1+4+4 =9

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Dividing by 10If the number ends with a 0

30 ÷ 10 = 3340 ÷ 10 = 3467 ÷ 10 = 6 R7784 ÷ 10 =78 R4

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Now You TryAre these numbers divisible by 10?

a) 5782b) 390c) 45

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Dividing by 11There is no special rule to help you know if a number

is divisible by 11…

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Now You TryAre these numbers divisible by 11?

a) 99

b) 88

c) 121

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REVIEW

Divisible by 1

Divisible by 2

Divisible by 3

Divisible by 4

Divisible by 5

Divisible by 6

Divisible by 7

Divisible by 8

Divisible by 9

Divisible by 10

Divisible by 11

Thumbs up if you remember the rule.

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After All… DIVISIBILITY Rules

Take Out Your Study Guide!!!

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RULES FOR DIVISIBILITY#1

A Number Is Divisible By: IF 2 3 4 5 6 8 910

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

The last 2 digits are divisible by 4

The sum of the digits is divisible by 3

The last digit is 0 or 5

It is divisible by 2 and 3

The last 3 digits are divisible by 8

The sum of the digits is divisible by 9

The last digit is 0

(÷2÷2÷2)

(÷2÷2)

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IS THE NUMBER DIVISIBLE EXACTLY BY?

WRITE yes (y) or no (n) REMEMBER: Show the sums for 3, and show the division for 4 and 8.

Number2 3 4 5 6 8 9 10

1)

360 y3+6 = 9

yy

y y

2)360180

2)180 90

yy y

2)6030

2)3015

2)90 45

#2