These are the few basic** divisibility rules** which every Mathematics lover should know. These **divisibility rules** will help in a faster calculation, thus saving a lot of time; especially in the exams.

## Divisibility Rules for 2

Contents

- 1 Divisibility Rules for 2
- 2 Divisibility Rules for 3
- 3 Divisibility Rules for 4
- 4 Divisibility Rules for 5
- 5 Divisibility Rules for 6
- 6 Divisibility Rules for 7
- 7 Divisibility Rules for 8
- 8 Divisibility Rule for 9
- 9 Divisibility Rule for 10
- 10 Divisibility Rules for 11
- 11 Divisibility Rules for 12
- 12 Divisibility Rules for 14
- 13 Divisibility Rules for 15
- 14 Divisibility Rule for 16
- 15 Divisibility Rule for 18
- 16 Divisibility Rule for 25
- 17 Divisibility Rule for 125

- If a number ends with either 0 or even digit, it is divisible by 2.
- Examples- 10, 32, 44, 56, 188 etc.

## Divisibility Rules for 3

- When the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
- Example- 4563 (Here sum of the digits i.e., 4+5+6+3=18 is divisible by 3 so the number must be divisible by 3).

## Divisibility Rules for 4

- When the number made by last two digits of the given number is divisible by 4.
- Also, if the number having two or more zeros at the end.
- Examples- 400, 8500, 754000, 564, 33832 etc.

## Divisibility Rules for 5

- Number ending with either 0 or 5 is divisible by 5
- Examples- 55, 15, 50, 65, 85 etc.

## Divisibility Rules for 6

- The number must be divisible by 2 and 3 both.
- Examples- 6, 12, 66, 72 etc.

## Divisibility Rules for 7

- When the difference between twice the digit at One’s Place and the number formed by other digits is either zero or a multiple of 7.
- Example- 658 is divisible by 7 i.e., (658 — 65 – 2*8 = 49 is divisible by 7).

## Divisibility Rules for 8

- If the number made by last three digits of a given number is divisible by 8.
- Also, if the number is having three or more zeros at the end.
- Examples- 9256, 65000, 895740000 etc.

## Divisibility Rule for 9

- When the sum of all digits of the given number is divisible by 9.
- Example- 85869 (8+5+8+6+9=36 is divisible by 9).

## Divisibility Rule for 10

- A number ending with zero is divisible by 10
- Examples- 10, 50, 5600, 450, 8886540 etc.

## Divisibility Rules for 11

- If the sums of digits at odd and even places are equal or differ by a number divisible by 11.
- Example- 2865432

Sum of digits at odd places 2+6+4+3=15

Sum of digits at even places 8+5+2= 15

Both are equal, so divisible by 11

- Example- 217382

Sum of digits at odd places 2+7+8=17

Sum of digits at even places 1+3+2= 6

Differ by 11 (17-6), so divisible by 11

## Divisibility Rules for 12

- If a number is divisible by both 4 and 3.
- Examples- 144, 3600, 2064 etc.

## Divisibility Rules for 14

- If the number is divisible by both 7 and 2.
- Example- 98, 15694 etc.

## Divisibility Rules for 15

- If the given number is divisible by 5 and 3 is also divisible by 15.
- Examples- 183555, 135 etc.

## Divisibility Rule for 16

- A number is divisible by 16 if number made by its last 4 digits is divisible by 16.
- Example- 126304 etc.

## Divisibility Rule for 18

- If a number is even and is divisible by 9, then it is divisible by 18.
- Examples- 108, 4356 etc.

## Divisibility Rule for 25

- If last two digits are either zero or divisible by 25.
- Examples- 75, 50, 13550, 1275 etc.

## Divisibility Rule for 125

- If the last three digits are divisible by 125.

Examples- 630125; Here last three digits 125 is divisible by 125, so the number 630125 is also divisible by 125.

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