## Divisibility Rules

Divisibility Rules are “tips and tricks” for recognising if a number is divisible by another.

Table of Contents

Using these tricks below can help you find factors of numbers and determine if a number is a prime.

### Divisibility by 2 Rule

## Is it divisible by 2?

Any **even** number is divisible by 2.

This can easily be determined by looking at the last digit – if it ends in 2, 4, 6, 8 or 0 then it is even, and therefore divisible by 2.

**Odd** numbers end in 1, 3, 5, 7 or 9, and are not divisible by 2.

Examples of numbers divisible by 2:

2**8**

5**0**

759**2**

Examples of numbers ** not** divisible by 2:

37

245

6829

### Divisibility by 3 Rule

## Is it divisible by 3?

If the sum of the digits of a number is a multiple of 3, then that number is divisible by 3.

Examples of numbers divisible by 3:

51 ( 5 + 1 = **6** )

147 ( 1 + 4 + 7 = **12** )

4392 ( 4 + 3 + 9 + 2 = **18** )

Examples of numbers ** not** divisible by 3:

73 ( 7 + 3 = 10 )

431 ( 4 + 3 + 1 = 8 )

6352 ( 6 + 3 + 5 + 2 = 16 )

### Divisibility by 4 Rule

## Is it divisible by 4?

If the last two digits of a number is divisible of 4, then that whole number is divisible by 4.

Examples of numbers divisible by 4:

7**16**

97**48**

573**24**

Examples of numbers ** not** divisible by 4:

8818

75614

956710

### Divisibility by 5 Rule

## Is it divisible by 5?

Another easy one to spot.

Examples of numbers divisible by 5:

7**5**

24**0**

896**5**

Examples of numbers ** not** divisible by 5:

87

649

5551

### Divisibility by 6 Rule

## Is it divisible by 6?

Know if divisible by 2 and by 3?

If a number is divisible by 2 AND divisible by 3, then that number is divisible by 6.

Examples of numbers divisible by 6:

7**2** ( 7 + 2 = **9** )

17**4** ( 1 + 7 + 4 = **12** )

532**8** ( 5 + 3 + 2 + 8 = **18** )

Examples of numbers ** not** divisible by 6:

### Divisibility by 8 Rule

## Is it divisible by 8?

If the last three digits of a number are divisible by 8, then that whole number is divisible by 8.

Examples of numbers divisible by 8:

5**216**

65**408**

997**552**

Examples of numbers ** not** divisible by 8:

45964

88698

157942

And how to know if the 3 digit number is divisible by 8? No easy spot, but either try using the bus-stop method, or try halving it, halving it again, and then halving one more time.

e.g. 216. Half of this is 108, half of that is 54. Half of 54 is 27, therefore 216 is divisible by 8.

### Divisibility by 9 Rule

## Is it divisible by 9?

If the sum of the digits of a number is a multiple of 9, then that number is divisible by 9.

Examples of numbers divisible by 9:

72 ( 7 + 2 = **9** )

486 ( 4 + 8 + 6 = **18** )

5985 ( 5 + 9 + 8 + 5 = **27** )

Examples of numbers ** not** divisible by 9:

93 ( 9 + 3 = 12 )

674 ( 6 + 7 + 4 = 17 )

8419 ( 8 + 4 + 1 + 9 = 22 )

### Divisibility by 10 Rule

## Is it divisible by 10?

Examples of numbers divisible by 10:

57**0**

382**0**

8483**0**

Examples of numbers ** not** divisible by 10:

105

4108

1025

And it follows, if a number ends in two 0s, it is divisible by 100 (e.g. 2300). If it ends in three 0s, then it is divisible by 1000 (e.g. 71000) etc.

### Divisibility by 11 Rule

## Is it divisible by 11?

If it is a two-digit number with the **same** digits, then that number is divisible by 11.

If the number has three or more digits, sum the alternate numbers and find the difference – if that difference is divisible by 11, then the number you started with is divisible by 11

Examples of numbers divisible by 11:

55 ( both digits are the same )

176 ( (1 + 6) – (7) = 0 and zero is divisible by 11 )

638 ( (6 + 8) – (3) = 11 )

6292 ( (6 + 9) – (2 + 2) = 11 )

45441 ( (4 + 4 + 1) – (5 + 4) = 0 )

Examples of numbers ** not** divisible by 11:

177 ( (1 + 7) – (7) = 1 )

8552 ( (8 + 5) – (5 + 2) = 6 )

74611 ( (7 + 6 + 1) – (4 + 1) = 9 )

## Is zero divisible by any number?

Zero is divisible by any number (except itself) so the answer is “Yes” to all the above questions.

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