## 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

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1. Chapter 3 Class 6 Playing with Numbers
2. Concept wise
3. Divisibility Tests - All

Divisibility Tests - All 