Question

Write the divisibility tests for 4, 5, 6, 8, 9, 10 and 11 giving your own examples for each.​

Answer 1

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 divisible by 4 212 is

• 1936 has last two digits 36

Since 36 is divisible by divisible by 4 1936 is

• 286 has last two digits 86

Since 86 is not divisible 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.

Divisibility by 6

A number is divisible by 6

• It is divisible by 2

• It is divisible by 3

Example:

• 36 is divisible by 2 as last digit is

6.

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if

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

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

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

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

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