Divisibility Tests - All

Chapter 3 Class 6 Playing with Numbers
Concept wise

## Divisibility by 1

Every number is divisible by 1, as (Any number)/1 = 1

Example:

1, 2, 2000, 30191, 193101 is divisible by 1

## Divisibility by 2

A number is divisible by 2, if last digit is 0, 2,  4, 6, 8

Example:

• 44 is divisible by 2 as last digit is 4
• 26 is divisible by 2 as last digit is 6
• 19 is not divisible by 2 as last digit is not 0, 2, 4, 6, 8

For video explanation with examples, see Divisibility by 2

## Divisibility by 3

If sum of digits of number is divisible by 3,

Then number is divisible by 3

Example:

• 18 has sum of digits 9, which is divisible by 3, so 18 is divisible by 3
• 39 has sum of digits 12, which is divisible by 3, so 39 is divisible by 3
• 93 has sum of digits 12, which is divisible by 3, so 93 is divisible by 3
• 25 has sum of digits 7, which is not divisible by 3, so 25 is not divisible by 3

For video explanation with examples, see Divisibility by 3

## Divisibility by 4

A number is divisible by 4

If its that two digits are divisible by 4

Example:

• 212 has last two digits 12
Since 12 is divisible by 4, 212 is divisible by 4
• 1936 has last two digits 36
Since 36 is divisible by 4, 1936 is divisible by 4
• 286 has last two digits 86
Since 86 is not divisible by 4, 286 is not divisible by 4

For video explanation with examples, see Divisibility by 4

## Divisibility by 5

A number is divisible by 5, if last digit is 5 or 0.

Example:

• 60 is divisible by 5 as last digit is 0
• 25 is divisible by 5 as last digit is 5
• 39 is not divisible by 5 as last digit is not 0 or 5

For video explanation with examples, see Divisibility by 5

## Divisibility by 6

A number is divisible by 6 if

• It is divisible by 2
• It is divisible by 3

Example:

• 36 is divisible by 2 as last digit is 6.
36 has sum of digits 9, which is divisible by 3, so 36 is divisible by 3
Since 36 is divisible by both 2 and 3, it is divisible by 6
• 27 is not divisible by 2 as last digit is not 0, 2, 4, 6, 8
27 has sum of digits 9, which is divisible by 3, so 36 is divisible by 3
Since 27 is not divisible by 2, it is not divisible by 6
• 216 is divisible by 2 as last digit is 6
216 has sum of digits 9, which is divisible by 3, so 216 is divisible by 3
Since 216 is divisible by both 2 and 3, it is divisible by 6

For video explanation with examples, see Divisibility by 6

## Divisibility by 7

If subtracting twice of last digit from the number formed by  remaining digits  is divisible by 7,

Then number is divisible by 7

Example:

• 371 has subtraction 37 – 2 × 1 = 35
Since 35 is divisible by 7
371 is divisible by 7
• 434 has subtraction 43 – 2 × 8 = 35
Since 35 is divisible by 7
434 is divisible by 7
• 905 has subtraction 90 – 2 × 5 = 80
Since 80 is not divisible by 7
905 is not divisible by 7

For video explanation with examples, see Divisibility by 7

## Divisibility by 8

A number is divisible by 8

If its last 3 digits are divisible by 8

Example:

• 9216 has last three digits 216
Since 216 is divisible by 8, 9216 is divisible by 8
• 2000 has last three digits 000 i.e. 0
Since 0 is divisible by 8, 2000 is divisible by 8
• 1416 has last three digits 416
Since 416 is not divisible by 8, 1416 is not Divisible by 8

For video explanation with examples, see Divisibility by 8

## Divisibility by 9

If sum of digits of number is divisible by 9,

Then number is divisible by 9

Example:

• 27 has sum of digits 9, which is divisible by 9, so 27 is divisible by 9
• 117 has sum of digits 9, which is divisible by 9, so 117 is divisible by 9
• 758 has sum of digits 20, which is not divisible by 9, so 758 is not divisible by 9

For video explanation with examples, see Divisibility by 9

## Divisibility by 10

A number is divisible by 10, if last digit is 0.

Example:

• 20 is divisible by 10 as last digit is 0
• 43 is not divisible by 10 as last digit is not 0

For video explanation with examples, see Divisibility by 10

## Divisibility by 11

If

So, if the difference is 0, 11, 22, 33, ….

Then, Number is divisible by 11

Example:

• 308 has sum odd = 11, sum even = 0, difference is 11.
Since 11 is divisible by 11,
∴ 308 is divisible by 11
• 1331 has sum odd = 4, sum even = 4, difference is 0.
Since difference is 0,
∴ 1331 is divisible by 11
• 5081 has sum odd = 1, sum even = 13, difference is 12.
Since 12 is not divisible by 11,
∴ 5081 is not divisible by 11

For video explanation with examples, see Divisibility by 11

## Divisibility by 12

A number is divisible by 12 if

• It is divisible by 3
• It is divisible by 4

Example:

• 1092 has sum of digits 12, which is divisible by 3, so 1092 is divisible by 3
1092 has last two digits 92, and 92 is divisible by 4, so 1092 is divisible by 4
Since 1092 is divisible by both 3 and 4, it is divisible by 12
• 648 has sum of digits 18, which is divisible by 3, so 648 is divisible by 3
648 has last two digits 48, and 48 is divisible by 4, so 648 is divisible by 4
Since 648 is divisible by both 3 and 4, it is divisible by 12
• 524 has sum of digits 11, which is not divisible by 3, so 524 is not divisible by 3
524 has last two digits 24, and 24 is divisible by 4, so 524 is divisible by 4
Since 524 is not divisible by 3, it is not divisible by 12

For video explanation with examples, see Divisibility by 12

## Divisibility by 13

If adding four times of last digit to number formed by remaining digits is divisible by 13,

Then number is divisible by 13

Example:

• 169 has addition 16 + 4 × 9 = 52
Since 52 is divisible by 13
169 is divisible by 13
• 247 has addition 24 + 4 × 7 = 52
Since 52 is divisible by 13
247 is divisible by 13
• 298 has addition 29 + 4 × 8 = 61
Since 61 is not divisible by 13
298 is not divisible by 13

For video explanation with examples, see Divisibility by 13

Made by

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.