 # Divisibility Rules

28th October, 2021

## Divisibility Rules

Divisibility Rules are “tips and tricks” for recognising if a number is divisible by another. Using these tricks below can help you find factors of numbers and determine if a number is a prime.

## Is it divisible by 2? Perhaps the most well-known divisibility rule.

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: 28

50

7592

Examples of numbers not divisible by 2: 37

245

6829

## 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 )

## 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: 716

9748

57324

Examples of numbers not divisible by 4: 8818

75614

956710

## Is it divisible by 5? Another easy one to spot.

If a number ends in a 5 or a 0, then that number is divisible by 5.

Examples of numbers divisible by 5: 75

240

8965

Examples of numbers not divisible by 5: 87

649

5551

## 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: 72 ( 7 + 2 = 9 )

174 ( 1 + 7 + 4 = 12 )

5328 ( 5 + 3 + 2 + 8 = 18 )

Examples of numbers not divisible by 6: 86 ( 8 + 6 = 14, divisible by 2 but not by 3 ) 369 ( 3 + 6 + 9 = 18, divisible by 3 but not by 2 ) 6794 ( 6 + 7 + 9 + 4 = 26, divisible by 2 but not by 3 )

## 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: 5216

65408

997552

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.

## 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 )

## Is it divisible by 10? Likely the easiest one to spot…
If a number ends in a 0, then that number is divisible by 10.

Examples of numbers divisible by 10: 570

3820

84830

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.

## Is it divisible by 11? This one is confusing to understand, but easier with examples.

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.