Number System: Divisibility tests (Divisibility by 2, divisibility by 3, divisibility by 4, divisibility by 5, divisibility by 6, divisibility by 7, divisibility by 8, divisibility by 9, divisibility by 10...)
Posted on : 14-02-2019 Posted by : Admin

If the last digit of a number is either 0 or even, then the number is divisible by 2.

Example:

14, 36, 892…

If the sum of digits of a number is divisible by 3, then the number is divisible by 3.

Example:

1533 1+5+3+3=12, which is divisible by 3, so 1533 must be divisible by 3.

If a number made by last two digits of a number is divisible by 4, then that particular number is divisible by 4 apart from this, the number having two or more zeros at the end is also divisible by 4.

Example:

7432 is divisible by 4 as the number made by its last two digits i.e. 32 is divisible by 4.

3500, 172000, 7530000… are divisible by 4 as they have two or more zeros at the end.

Numbers having 0 or 5 at the end are divisible by 5.

Example:

35, 1320, 245… are divisible by 5 as they have 0 or 5 at the end.

If a number is divisible by both 3 and 2, then that particular number is divisible by 6 also.

Example:

24, 42, 720… are divisible by 6 as they are divisible by both 3 and 2.

A number is divisible by 7, if the difference between twice the digit at ones place and the number formed by other digits is either 0 or a multiple of 7.

Example:

658 is divisible by 7 because 65-2×8=65-16=49

As 49 is divisible by 7, the number 658 is also divisible by 7

If the number made by last three digits of a number is divisible by 8, then the number is also divisible by 8 apart from this, if the last three or more digits of a number is zeros, then the number is divisible by 8.

Example:

2256 As 256 (the last three digits of 2256) is divisible by 8, therefore 2256 is also divisible by 8.

If the sum of all the digits of a number is divisible by 9, then the number is also divisible by 9.

Example:

3465 3+4+6+5=18 which is divisible by 9 hence 3465 is also divisible by 9.

If a number ends with zero, then it is divisible by 10.

Example:

10, 30, 50 … are divisible by 10 as these all end with 0.

If the sums of digits at odd and even places are equal or differ by a number divisible by 11, then the number is also divisible by 11.

Example:

2568324

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

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

Both are equal, hence 2568324 is divisible by 11

A number which is divisible by both 4 and 3 is also divisible by 12.

Example:

1248 is divisible by both 3 and 4. Therefore it is divisible by 12 also.

A number which is divisible by both 7 and 2 is also divisible by 14.

Example:

1232 is divisible by both 7 and 2. Therefore it is divisible by 14 also.

A number which is divisible by both 5 and 3 is divisible by 15 also.

Example:

1575 is divisible by both 5 and 3. Therefore it is divisible by 15 also.

A number is divisible by 16 when the number made by its last four digits is divisible by 16

Example:

186304 is divisible by 16 as the number made by its last 4 digits is divisible by 16

A number is divisible by 18 when it is even and divisible by 9.

Example:

639198 is divisible by 18 as it is even and divisible by 9

A number is divisible by 25 when its last two digits are either zero or divisible by 25.

Example:

500, 1275 are divisible by 25 as last two digits of these numbers are either zero or divisible by 25.

A number is divisible by 125 if the number made by its last 3 digits is divisible by 125.

Example:

425125 is divisible by 125 as the number made by its last 3 digits are divisible by 125