Divisibility Rules
Divisibility rules are quick tests that show whether a number divides exactly by another without doing a full division.
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Divisibility rules are quick tests that show whether a number divides exactly by another without doing a full division.
- A number is divisible by 3 if its digit sum is
- Divisible by 4 if the last two digits are
- Divisible by 5 if it ends in 0 or 5
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Divisibility Rules?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Divisibility Rules. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Divisibility Rules in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Divisibility Rules gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Divisibility Rules in detail
Divisibility rules are quick tests that tell you whether one number divides another without doing the division. A number is divisible by 2 if it ends in an even digit, by 5 if it ends in 0 or 5, by 3 if its digits sum to a multiple of 3, and by 9 if its digits sum to a multiple of 9.
Further rules cover 4 (last two digits), 6 (divisible by both 2 and 3) and 10 (ends in 0). These shortcuts make factorising, simplifying fractions and checking for primes much faster, and they are handy for spotting errors in long calculations.
How the interactive helps you understand Divisibility Rules
Click a card to flip it and reveal the answer, then move on to the next one.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Divisibility Rules.
Real-life uses and examples
- Use Divisibility Rules when comparing prices, discounts or recipe quantities in everyday life.
- Explain Divisibility Rules to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Divisibility Rules in exam questions, where it often sits inside a short word problem.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Divisibility Rules.
- Memorising the steps for Divisibility Rules without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Divisibility Rules
What is Divisibility Rules?
Divisibility rules are quick tests that show whether a number divides exactly by another without doing a full division.
What are the most important points about Divisibility Rules?
The main points are: A number is divisible by 3 if its digit sum is; Divisible by 4 if the last two digits are; Divisible by 5 if it ends in 0 or 5.
Why is Divisibility Rules useful?
Understanding Divisibility Rules gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Divisibility Rules?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Divisibility Rules?
Related topics in Mathematics include Fractions, Multiplying and Dividing Fractions, Converting Fractions and Decimals.