divisibility

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


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!


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..


Dividing By 1All numbers are divisible by 1


Now You TryAre these numbers divisible by 1?

a) 578b) 1201c) 465


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



a) 458b) 1279c) 759

Not an even number

Not an even number


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.



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

b) 56 Sum of 5+6 =11 NO

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


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



a) 584

b) 261

4)84 21

4)61 15 r1 NO

Take the last 2 digits and divide by 4


Dividing by 5If the number ends in 5 or 0

25 ÷ 5 = 5 23 ÷ 5 = 4 R3 NO



a) 554

b) 6890

c) 345


Dividing by 6If the number is divisible by 2,

AND . . .

If the number is divisible by 3



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


Dividing by 7

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



a) 500b) 49c) 2100


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.



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


Dividing by 9Similar to dividing by 3

Add up digits

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


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 =



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


Dividing by 10If the number ends with a 0

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



a) 5782b) 390c) 45


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

is divisible by 11…



a) 99

b) 88

c) 121


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.


After All… DIVISIBILITY Rules

Take Out Your Study Guide!!!


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)


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

divisibility

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