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Number Theory
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India
Class VI

Divisibility tests

Lesson
Practice
Lesson

"Divisible by" means "when you divide one number by another the result is a whole number." For example $$77is divisible by $$7 because $$77÷​7=11. We could also say that $$7 and $$11 are factors of $$77 (see Breaking Down Numbers for more information on factors).

Remember, we can use our knowledge of multiplication and division to complete sets of related number facts.

Example

$$13×4=52

$$4×13=52

$$52÷​4=13

$$52÷​13=4

 

Quick checks of divisibility

Divisible by 2

All even numbers are divisible by $$2.

Example

$$28 is even, so it is divisible by $$2.

$$28÷​2=14

 

Divisibility by 3

A number is divisible by $$3 if the sum of the digits is divisible by $$3.

Example

$$234 is divisible by $$3 since $$2+3+4=9.

$$234÷​3=78

 

Divisibility by 5

All numbers ending with a $$5 or a $$0 are divisible by $$5.

Example

$$85 ends with a $$5, so it is divisible by $$5.

$$85÷​5=17

 

Divisibility by 9

A number is divisible by $$9 if the sum of the digits is divisible by $$9.

Example

$$324 is divisible by $$9 since $$3+2+4=9

$$324÷​9=36

 

Divisibility by 10

All numbers ending in a 0 are divisible by 10.

Example

$$5200 ends in a $$0, so it is divisible by $$10.

$$5200÷​10=520

Worked Examples

Question 1

Are the following numbers divisible by $$4?

  1. $$58784

    Yes

    A

    No

    B

  2. $$372938

    Yes

    A

    No

    B

  3. $$58832

    Yes

    A

    No

    B

   

Question 2

Which of the following numbers are exactly divisible by 3?

  1. $$73500

    A

    $$73495

    B

  2. $$545824

    A

    $$599772

    B

 

 

Question 3

 

Are the following numbers divisible by $$8?

  1. $$195992

    Yes

    A

    No

    B

  2. $$1669488

    Yes

    A

    No

    B

  3. $$1669374

    Yes

    A

    No

    B
  

 
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