*This page was created using ideas from Doug Ray at www.academicmeet.com

A
number is divisible by another number if after dividing, the remainder is zero.
For example, 18 is divisible by 3 because 18 ๗* *3 = 6 with 0
remainder. However, 25 is not
divisible by 4 because 25 ๗* *4 = 6 with a remainder of 1.
There are several mental math tricks that can be used to find the
remainder after division without actually having to do the division.

To navigate to a certain divisibility rule click on the corresponding number:

[2][3][4][5][6][7][8][9][10][11][12]

**Dividing By 2**:
A number is divisible by 2 if the last digit is even.

**Dividing By 3**:
A number is divisible by 3 if the sum of all the digits is divisible by
3.

Ex [1] 34,164 is divisible by 3 because 3+4+1+6+4 = 18 which is divisible by 3.

*To find the remainder of a number divided by 3, add the digits and find that remainder. So if the digits added together equal 13 then the number has a remainder of 1 since 13 divided by 3 has a remainder of 1.

**Dividing By 4**:
A number is divisible by 4 if the last 2-digits are divisible by 4.

Ex [1] 34,164 is divisible by 4 because 64 is divisible by 4.

*To find the remainder of a number divided by 4 take the remainder of the last 2 digits. So if the last 2-digits are 13 then the number has a remainder of 1 since 13 divided by 4 has a remainder of 1.

**Dividing By 5**:
A number is divisible by 5 if the last digit is a 5 or a 0.

*To find the remainder of a number divided by 5 simply use the last digit. If it is greater than 5, subtract 5 for the remainder.

**Dividing By 6**:
A number is divisible by 6 if it is divisible by 2 and by 3.

Ex [1] 34,164 is divisible by 6 because it is divisible by 2 and 3. *See above

**Dividing By 7**:
A number is divisible by 7 if the following is true:

1. Multiply the ones digit by 2.

2. Subtract this value from the rest of the number.

3. Continue this pattern until you find a number you know is or is not divisible by 7.

Ex [1] 7203 is divisible by 7 because

a) 2 x 3 = 6.

b) 720 6 = 714 which is divisible by 7.

Ex [2] 14443 is not divisible by 7 because

a) 3 x 2 = 6.

b) 1444 6 = 1438.

c) 8 x 2 = 16.

d) 143 16 = 127 which is not divisible by 7.

Note: This method takes a lot of practice and is sometimes easier to just work it out individually.

**Dividing By 8**:
A number is divisible by 8 if the last 3-digits are divisible by 8.

Ex [1] 34,168 is divisible by 8 because 168 is divisible by 8.

*To find the remainder of a number divided by 8 take the remainder of the last 3-digits. So if the last 3-digits are 013 then the number has a remainder of 5.

**Dividing By 9**:
A number is divisible by 9 if the sum of the digits is divisible by 9.

Ex [1] 34,164 is divisible by 9 because 3+4+1+6+4 = 18 which is divisible by 9.

*To find the remainder of a number divided by 9, add the digits and find that remainder. So if the digits added together equal 13 then the number has a remainder of 4 since 13 divided by 9 has a remainder of 4.

**Dividing By 10**:
A number is divisible by 10 if the last digit is a 0.

*To find the remainder of a number divided by 10 simply use the last digit.

**Dividing By 11**:
A number is divisible by 11 if this is true:

1^{st}
Step: Starting from the ones digit add every other digit

2^{nd} Step: Add
the remaining digits together

3^{rd} Step: Subtract
1^{st} Step from the 2^{nd} Step

*If this value is 0 then the number is divisible by 11. If it is not 0 then this is the remainder after dividing by 11 if it is positive. If the number is negative add 11 to it to get the remainder.

Ex [1] 6613585 is divisible by 11 since (5+5+1+6) (8+3+6) = 0.

**Dividing By 12**:
A number is divisible by 12 if it is divisible by 3 and by 4.

Ex [1] 34,164 is divisible by 12 because it is divisible by 3 and 4. *See Above