Divisibility Checker
See if a number divides evenly, and which common rules apply.
Divisibility Checker
Check if numbers are divisible and learn the mathematical rules behind divisibility
Divisibility Rules Reference
Rule of 2
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8)
Rule of 3
A number is divisible by 3 if the sum of its digits is divisible by 3
Rule of 4
A number is divisible by 4 if its last two digits form a number divisible by 4
Rule of 5
A number is divisible by 5 if its last digit is 0 or 5
Quick Examples
What divisibility means
A is divisible by B when A ÷ B leaves remainder 0. Then B is a factor of A, and A is a multiple of B.
Rules for 2, 3, 5, 9, 10 (and friends) exploit base-10 digit tricks so you can skip long division.
Common rules (base 10)
- 2: last digit even
- 3 / 9: digit sum divisible by 3 / 9
- 5 / 10: ends in 0 or 5 / ends in 0
- 4: last two digits form a number divisible by 4
- 6: divisible by both 2 and 3
- 8: last three digits divisible by 8
- 11: alternating digit sum divisible by 11
Where it shows up
- Fraction simplify / common denominators
- Mental checks before trusting a calculator
- Code:
n % d === 0is the same idea
Frequently Asked Questions
Why do divisibility rules work?
They follow from modular arithmetic in base 10. Example: 10 ≡ 1 (mod 9), so digit sums track divisibility by 9.
Are there rules for every number?
In theory yes; for large divisors, modulo or a calculator is usually easier than a hand rule.
Divisibility vs factors?
Divisibility is the relationship; factors are the numbers that divide. Same coin, two faces.
Negative numbers?
Use absolute values for the usual school rules. −24 is divisible by 3 because 24 is.
Which rule to learn first?
2, then 5/10, then 3/9. Those cover most everyday cases.
Other bases?
Rules depend on the base. In binary, divisible by 2 means the last bit is 0.
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