**Divisibility Rules**

These **divisibility rules** will help in a faster calculation, thus saving a lot of time; especially in the exams.

**Divisibility Rules for 2**

- 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 the 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 the 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 the 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 the 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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