Divisibility Rules (2-12)

Front

Divisibility rule for 2

Back

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8).

Ex: 478
ends with the digit 8,
therefore 478 is even and is divisible by 2.

Front

Divisibility rule for 3

Back

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

Ex: 126;

1+2+6=9.
9 is a multiple of 3, therefore 126 is divisible by 3.

(You can repeat this process if needed when the sum of the digits is not an obvious multiple of 3. You can repeatedly add the digits of the sums until you can check if the number is a multiple of 3.

Ex: 76,887,694,143,612;

7+6+8+8+7+6+9+4+1+4+3+6+1+2=72,

7+2=9.
9 is a multiple of 3, therefore 76,887,694,143,612 is divisible by 3.)

Front

Divisibility rule for 4

Back

A number is divisible by 4 if the last two digits form a number divisible by 4

OR

The number ends in 00.

Ex: 4,736;
4,736 ends with 36.
36/4 = 9, so 36 is divisible by 4,
& therefore 4,736 is divisible by 4.

Ex: 4,736;
4,736 ends with 36.
36/2 = 18 --> 18/2 = 9 --> therefore 36/4 = 9,
so 36 is divisible by 4,
& therefore 4,736 is divisible by 4.

OR

Ex: 1,300.

1,300 ends with 00.
Therefore, 1,300 is divisible by 8.

Front

Divisibility rule for 5

Back

A number is divisible by 5 if its last digit is 0 or 5.

Ex: 47,835;
47,835 ends in a 5,
therefore 47,835 is divisible by 5.

Ex: 6,430;

6,430 ends in a 0,
therefore 6,430 is divisible by 5.

Front

Divisibility rule for 6

Back

A number is divisible by 6 if it is divisible by the rules for both 2 AND 3.

Ex: 456;

Rule for 2 --> 456 ends in a 6,
which is even, therefore, 456 is divisible by 2.

Rule for 3 --> 4+5+6=15.
15 is divisible by 3,
therefore, 456 is divisible by 3.

456 is divisible by BOTH 2 AND 3,
therefore 456, is divisible by 6.

Front

Divisibility rule for 7

Back

To check divisibility by 7, double the last digit and subtract it from the rest of the number; if the result is 0 or a number that is divisible by 7 (positive, negative or zero), it works.

Repeat the process as many times as necessary until you get to a value that is reasonable (a value under 84 because 7 x 12 = 84).

Ex: 1,659;

9×2=18, 165-18=147.

7×2=14, 14-14=0. 

0 is a multiple of 7,  therefore 1,659 is divisible by 7.

Front

Divisibility rule for 8

Back

A number is divisible by 8 if the last three digits form a number divisible by 8

OR

the number ends in 000.

Ex: 245,768;

245,768 ends with 768.
768/2 = 384 --> 384/2 = 150+42 = 192 -->
192/2 = 50+46 = 96 --> Therefore, 768/8 = 96,
so, 768 is divisible by 8,
therefore, 245,768 is divisible by 8.

OR

Ex: 12,000.

12,000 ends with 000.
Therefore, 12,000 is divisible by 8.

Front

Divisibility rule for 9

Back

A number is divisible by 9 if the sum of its digits is divisible by 9.

EX: 59,364;

5+9+3+6+4=27.
27 is a multiple of 9,
therefore, 59,364 is divisible by 9.

(You can repeat this process if needed when the sum of the digits is not an obvious multiple of 9. You can repeatedly add the digits of the sums until you can check if the number is a multiple of 9.)

Front

Divisibility rule for 10

Back

A number is divisible by 10 if its last digit is 0.

Ex: 495,430;

495,430 ends in a 0,
therefore 495,430 is divisible by 10

Front

Divisibility rule for 11

Back

The difference between the sum of the digits in odd positions and the sum of the digits in even positions is a multiple of 11 or is 0 (positive, negative or zero).

Step 1: Take the sums of alternating digits.

Step 2: Subtract the sums. (Sum of Odd Position Digits - Sum of Even Position Digits)

Step 3: The difference (answer to the subtraction above) is either a 0 or is a multiple of 11.

Ex: 40,194;

4-0+1-9+4=0.
0 is a multiple of 11, therefore, 40,194 is divisible by 11.