Divisibility Checker

See if a number divides evenly, and which common rules apply.

Divisibility Rules
Number Theory
Modular Arithmetic

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 === 0 is 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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