Welcome to our Divisibility Rules 1-10 Chart page.

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- A number is divisible by another number if it can be divided by the other number with no remainder.
- So n is divisible by p if n ÷ p is a whole number with no remainder.

We can also say that a number is divisible by another number if it can be made by multiplying the other number by another whole number.

- So n is divisible by p if n is in the p times table.

We can also say that n is divisible by p if:

- p is a factor of n;
- n is a multiple of p.

There are some quick ways to test whether numbers are divisible which make life easier.

If you have a calculator, you can quickly test divisibility by dividing one number by the other and seeing if there is a remainder.

For example, we can tell that 3268 is divisible by 4 because 3268 ÷ 4 = 817.

We can tell that 4186 is not divisible by 4 because 4186 ÷ 4 = 1046.5. As there is a decimal part to the answer, it shows there is a remainder.

However, if we don't have a calculator, you can always test for divisibility using long division (which can be quite slow).

There are some quick and easy ways to test for divisibility by numbers from 1 to 10.

Number | Divisibility Rule | Example |
---|---|---|

## 1 |
Any integer (positive or negative whole number). |
425 is divisible by 1. 13.8 is not divisible by 1. |

## 2 |
Any even integer - a number whose last digit is 0, 2, 4, 6 or 8. |
126 is divisible by 2. 3275 is not divisible by 2. |

## 3 |
Any integer where the sum of the digits is a multiple of 3. |
4365 is divisible by 2 because 4+3+6+5=18 which is divisible by 3. 3217 is not divisible by 2 because 3+2+1+7=13 which is not divisible by 3. |

## 4 |
Any even integer whose last two digits are divisible by 4. A quick way of testing this is to halve the last two digits twice and see if you get a whole number. |
2956 is divisible by 4 because 56 is divisible by 4 (half of 56 = 28 and half of 28=14). 3122 is not divisible by 4 because half of 22 is 11 and half of 11 is 5 ½. 8179 is not divisible by 4 because it is odd. |

## 5 |
Any integer whose last digits is a 0 or a 5. |
1975 is divisible by 5 because it ends in a 5. 6249 is not divisible by 5 because it ends in a 9. |

## 6 |
Any even integer which is divisible by 3. |
5244 is divisible by 6 because it is even and 5+2+4+4=15 which is divisible by 3 (15 ÷ 3 = 5). 2859 is not divisible by 6 because it is odd. 1093 is not divisible by 6 because 1+0+9+3=13 which is not divisible by 3. |

## 7 |
Double the first digit and subtract this result from the number made by the other digits. If this is divisible by 7, then the number is divisible by 7. This process can be repeated for larger numbers. |
2674. 267 - 2x4 = 259. Repeat 25 - 2x9 = 7. This number is divisible by 7. 3129. 312 - 2x9 = 294. Repear 29 - 2x4 = 21 = 7x3. This number is divisible by 7. 876. 87 - 2x6 = 75. This number is not divisible by 7 since 75 ÷ 7 = 10 |

## 8 |
Any even integer whose last 3 digits are divisible by 8. A quick way of testing this is to halve the last 3 digits three times and see if you get a whole number. |
5240 is divisible by 8 because half of 240=120, half of 120=60 and half of 60=30 2179 is not divisible by 8 because it is odd. 2164 is not divisible by 8 because half of 2164 = 1082, half of 1082 = 541 and half of 541 = 270.5 (not a whole number) |

## 9 |
Any integer where the sum of digits is divisible by 9. |
6273 is divisible by 9 because 6+2+7+3=18 which is divisible by 9. 5031 is divisible by 9 because 5+0+3+1=9 which is divisible by 9. 2884 is not divisible by 9 because 2+8+8+4=22 which is not divisible by 9. |

## 10 |
Any integer whose last digit is 0. |
7890 is divisible by 10 because it ends in a 0. 3210 is divisible by 10 beacuse it ends in a 0. 2815 is not divisible by 10 because it ends in a 5. |

We have several pre-prepared divisibilty rules charts for you to print.

There are a variety of charts, both portrait and landscape, which include worked examples.

These first two charts include divisibility rules for numbers 1 to 10 along with odd and even numbers.

These two charts just have divisibility rules for numbers 1 to 10.

There are 2 mini charts with divisibility rules on each page. The charts just have the basic rules with no examples.

These first two charts include divisibility rules for numbers 1 to 10 along with odd and even numbers.

Take a look at some more of our worksheets similar to these.

We have a selection of divisibility rules worksheets to help you practice your knowledge.

There is also an online quiz for you to try!

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