Divisibility Test Calculator

Test if a number is divisible by 2 through 12 and other common divisors. See which divisibility rules apply with step-by-step explanations.

Enter a Number

Result

Divisors Found (2-12)
8
out of 11 tested

Step-by-Step Divisibility Rules

360 is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12

Understanding Divisibility Rules

Divisibility rules are shortcuts that help you quickly determine whether a number can be evenly divided by another number without performing the full division. These rules are fundamental in number theory and are widely used in mental math, simplifying fractions, and finding factors.

Common Divisibility Rules

Divisible by 2

A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

Last digit is even

Divisible by 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Digit sum divisible by 3

Divisible by 4

A number is divisible by 4 if its last two digits form a number divisible by 4.

Last 2 digits divisible by 4

Divisible by 5

A number is divisible by 5 if its last digit is 0 or 5.

Last digit is 0 or 5

Divisible by 6

A number is divisible by 6 if it is divisible by both 2 and 3.

Divisible by 2 AND 3

Divisible by 7

Double the last digit and subtract from the rest. If the result is divisible by 7, so is the original.

Double last, subtract from rest

Divisible by 8

A number is divisible by 8 if its last three digits form a number divisible by 8.

Last 3 digits divisible by 8

Divisible by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Digit sum divisible by 9

Divisible by 10

A number is divisible by 10 if its last digit is 0.

Last digit is 0

Divisible by 11

Alternate adding and subtracting digits from left to right. If the result is divisible by 11, so is the number.

Alternating sum divisible by 11

Divisible by 12

A number is divisible by 12 if it is divisible by both 3 and 4.

Divisible by 3 AND 4

Why Divisibility Rules Matter

Divisibility rules are essential building blocks in mathematics. They help students and professionals simplify fractions, find greatest common divisors (GCD), determine least common multiples (LCM), and perform prime factorization. In competitive mathematics, knowing these rules can save significant time.

Practical Applications

  • Simplifying fractions quickly without a calculator.
  • Checking answers to multiplication and division problems.
  • Finding factors and prime factorizations of large numbers.
  • Solving problems in modular arithmetic and cryptography.
  • Everyday tasks like splitting bills evenly among a group.

Tips for Using Divisibility Rules

  • Start with the easiest rules (2, 5, 10) and work toward the harder ones (7, 11).
  • Combine rules: if a number is divisible by both 2 and 3, it is divisible by 6.
  • For very large numbers, apply the digit-sum rules for 3 and 9 first.
  • Practice mental math regularly to internalize these shortcuts.