Divisibility Rules
Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
Key idea
Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
In depth
Quick tests tell you if a number divides evenly without dividing. They come from how place values behave: 2 (even last digit), 3 (digit sum divisible by 3), 5 (ends 0 or 5), 9 (digit sum divisible by 9), 10 (ends in 0).
Worked example
Is 4,527 divisible by 3? 4+5+2+7 = 18, which is divisible by 3, so yes.
Real-world uses
- Quickly checking whether a large number like a bank account or ISBN is divisible
- Simplifying fractions
Common mistake
Applying the digit-sum rule to 4 or 8; those depend on the last two or three digits.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Divisibility Rules?
Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9. It is a topic at the intermediate level in Arithmetic & Number Sense.
Where is Divisibility Rules used in real life?
Real-world examples: Quickly checking whether a large number like a bank account or ISBN is divisible; Simplifying fractions.
What should I learn before Divisibility Rules?
Make sure you are comfortable with Factors and Multiples, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Divisibility Rules?
Applying the digit-sum rule to 4 or 8; those depend on the last two or three digits.
How can I practise Divisibility Rules?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Divisibility Rules?
Move on to Prime Numbers next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.
- Prime Factorization – Every integer above 1 is a unique product of primes.