Divisibility Rules of Numbers

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.