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In addition to the revision notes for Divisibility Rules on this page, you can also access the following Arithmetic learning resources for Divisibility Rules

Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
---|---|---|---|---|---|---|

1.6 | Divisibility Rules |

In these revision notes for Divisibility Rules, we cover the following key points:

- What does divisibility mean?
- How do we write in symbols when a number is divisible by another number?
- What are the divisibility rules for the numbers from 1 to 20?
- What are relatively prime numbers?
- How do relatively prime numbers determine some of divisibility rules?

An integer x is divisible by another integer y if the result of x ÷ y is another integer, i.e. it is a number without remainder (r = 0). We write the symbol (⁝) to represent the divisibility of two numbers.

The **divisibility by 1 rule** states that all numbers are divisible by 1.

The **divisibility by 2 rule** states that the number must be even in order to be divisible by 2.

The **divisibility by 3 rule** states that the sum of digits of the original number must be divisible by 3.

The **divisibility by 4 rule** states that the last two digits of the original number must form a number divisible by 4.

The **divisibility by 5 rule** states that a number must end with 0 or 5.

The **divisibility by 6 rule** states that a number must be divisible by 2 and 3 at the same time in order to be divisible by 6.

The **divisibility by 7 rule** states that a number is divisible by 7 if the difference between twice the value of the digit in the ones place and the number formed by the rest of the digits is either 0 or a multiple of 7.

The **divisibility by 8 rule** states that the last three digits of the original number must form a number that is divisible by 8.

The **divisibility by 9 rule** states that the sum of digits of the original number must be divisible by 9.

The **divisibility by 10 rule** states that the number must end with zero to be divisible by 10.

The **divisibility by 11 rule** states that a number is divisible by 11 if the difference between the sum of the digits in the odd place value and even place value is a multiple of 11 (including 0).

The **divisibility by 12 rule** states that a number must be divisible by both 3 and 4 to be divisible by 12.

The **divisibility by 13 rule** states that a number is divisible by 13 if after grouping the digits in groups of three starting from the rightmost place value and applying the subtraction and addition of the numbers obtained by these groups alternatively from right to left, we obtain a number divisible by 13, including 0.

The **divisibility by 14 rule** states that a number is divisible by 14 if it is divisible by both 2 and 7.

The **divisibility by 15 rule** states that a number is divisible by 15 if it is divisible by both 3 and 5.

The **divisibility by 16 rule** states that a number is divisible by 16 if the last three digits form a number that is divisible by 16 while the fourth last digit is even.

The **divisibility by 17 rule** states that a number is divisible by 17 if after multiplying the last digit by 5 and subtract it from the rest, the result is divisible by 17.

The **divisibility by 18 rule** states that a number is divisible by 18 if it is divisible by both 2 and 9.

The **divisibility by 19 rule** states that a number is divisible by 19 if twice the last digit plus the rest of number give a number divisible by 19.

The **divisibility by 20 rule** states that a number is divisible by 20 if the last two digits of the original number are a multiple of 20.

Two numbers are relatively prime when they don't have any other common factor besides 1. In general, if a number is divisible by each of two relatively prime numbers, it is also divisible by their product.

Enjoy the "Divisibility Rules" revision notes? People who liked the "Divisibility Rules" revision notes found the following resources useful:

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- Arithmetic Math tutorial: Divisibility Rules. Read the Divisibility Rules math tutorial and build your math knowledge of Arithmetic
- Arithmetic Video tutorial: Divisibility Rules. Watch or listen to the Divisibility Rules video tutorial, a useful way to help you revise when travelling to and from school/college
- Arithmetic Practice Questions: Divisibility Rules. Test and improve your knowledge of Divisibility Rules with example questins and answers
- Check your calculations for Arithmetic questions with our excellent Arithmetic calculators which contain full equations and calculations clearly displayed line by line. See the Arithmetic Calculators by iCalculator™ below.
- Continuing learning arithmetic - read our next math tutorial: Decimal Number System and Operations with Decimals

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