## Divisibility by 2 Rule

Almost everyone is familiar with this rule which states that any even number can be divided by 2. Even numbers are multiples of 2. A number is even if ends in 0,2,4,6, or 8.

**Ex**.

- 2
- 0
- 4
- -2
- -312
- 31,102

## Divisibility by 3 Rule

Add up all the digits in the number. Find out what the sum is. If the sum is divisible by 3, so is the number

**Ex**.

12→1 + 2 = 3 And 3 is divisible by 3 so the number 12 is also divisible by 3.

## Divisibility by 4 Rule

A number is divisible by 4 if the number's last two digits are divisible by 4.

**Ex**.

358912 ends in 12 which is divisible by 4, thus so is 358912

## Divisibility by 5 Rule

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

**Ex**.

- 10 → since the last digit is 0, 10 satisfies this rule and is divisible by 5
- 15 → since the last digit is 5, 15 satisfies this rule and is divisible by 5
- 45
- -30
- 55
- -105

## Divisibility by 6 Rule

If the Number is divisible by 2 and 3 it is divisible by 6 also.

**Ex**.

114 → satisfies both conditions

- 1) 1+1+4 = 6 which is divisible by 3
- 2) 114 is even so divisible by 2
- Hence 114 is divisible by 6

## Divisibility by 7 Rule

**Test - 1**

**Ex**

357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.

**Test - 2**

**Ex**

Example: Is 2016 divisible by 7? 6(1) + 1(3) + 0(2) + 2(6) = 21 21 is divisible by 7 and we can now say that 2016 is also divisible by 7

## Divisibility by 8 Rule

A number passes the test for 8 if the last three digits form a number is divisible 8.

**Ex**.

6008 - The last 3 digits are divisible by 8, therefore, so is 6008.

## Divisibility by 9 Rule

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

**Ex**.

43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

## Divisibility by 10 Rule

A number passes the test for 10 if its final digit is 0.

**Ex**.

- 100
- 110
- -110
- 1,320,320.

## Divisibility by 11 Rule

A number passes the test for 11 if the difference of the sums of alternating digits is divisible by 11.

**Ex**.

- 682 → (6+2) - 8 = 0 which is, of course, evenly divided by 11 so 682 passes this divisibility test
- 10,813 → (1+8+3) - (0+1) = 12-1 =11. Yes, this satisfies the rule for 11!
- 25, 784 = → (2+ 7 + 4) - (5+8) = 13 - 13 =0 . Yes this also satisfies the rule for 11!