# Divisibility tests

Lesson

"Divisible by" means "when you divide one number by another the result is a whole number." For example $77$77is divisible by $7$7 because $77\div7=11$77÷​7=11. We could also say that $7$7 and $11$11 are factors of $77$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\times4=52$13×4=52

$4\times13=52$4×13=52

$52\div4=13$52÷​4=13

$52\div13=4$52÷​13=4

## Quick checks of divisibility

Divisible by 2

All even numbers are divisible by $2$2.

#### Example

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

$28\div2=14$28÷​2=14

Divisibility by 3

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

#### Example

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

$234\div3=78$234÷​3=78

Divisibility by 5

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

#### Example

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

$85\div5=17$85÷​5=17

Divisibility by 9

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

#### Example

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

$324\div9=36$324÷​9=36

Divisibility by 10

All numbers ending in a 0 are divisible by 10.

#### Example

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

$5200\div10=520$5200÷​10=520

#### Worked Examples

##### Question 1

Are the following numbers divisible by $4$4?

1. $58784$58784

Yes

A

No

B

Yes

A

No

B
2. $372938$372938

Yes

A

No

B

Yes

A

No

B
3. $58832$58832

Yes

A

No

B

Yes

A

No

B

##### Question 2

Which of the following numbers are exactly divisible by 3?

1. $73500$73500

A

$73495$73495

B

$73500$73500

A

$73495$73495

B
2. $545824$545824

A

$599772$599772

B

$545824$545824

A

$599772$599772

B

##### Question 3

Are the following numbers divisible by $8$8?

1. $195992$195992

Yes

A

No

B

Yes

A

No

B
2. $1669488$1669488

Yes

A

No

B

Yes

A

No

B
3. $1669374$1669374

Yes

A

No

B

Yes

A

No

B

### Outcomes

#### NA4-1

Use a range of multiplicative strategies when operating on whole numbers