Math July 13, 2026 · 8 Min Read

Divisibility Test Calculator – Guide & Formulas

Test if a number is divisible by 2 through 12 instantly. Check divisibility rules with step-by-step explanations and factor identification.

Test if a number is divisible by 2 through 12 instantly. Enter any integer to check all divisibility rules with step-by-step explanations for each divisor.

Key Takeaway

Use the free Divisibility Test Calculator to test if a number is divisible by 2 through 12 instantly. check divisibility rules with step-by-step explanations and factor identification. Get instant results with step-by-step explanations.

How to Use the Divisibility Test Calculator

  1. Enter any positive or negative whole number into the input field.
  2. Review the divisibility results for each divisor from 2 through 12.
  3. Click on any divisor to see the detailed divisibility rule and verification.
  4. Check the prime factorization to understand which divisors are factors of the number.

The Formula

A number n is divisible by d if and only if n mod d = 0 (no remainder). Key rules: Divisible by 2 if even, by 3 if digit sum divisible by 3, by 5 if ends in 0 or 5, by 7 by doubling last digit and subtracting, by 11 by alternating sum of digits.

Variable Definitions

  • n: The number being tested for divisibility
  • d: The divisor (2 through 12)
  • n mod d: The remainder when n is divided by d
  • Digit sum: The sum of all digits in the number

Testing Divisibility of 378

Check which numbers from 2 to 12 divide evenly into 378.

  1. Step 1: Divisible by 2? 378 is even (ends in 8). Yes ✓
  2. Step 2: Divisible by 3? Sum of digits = 3+7+8 = 18. Since 18÷3 = 6, yes ✓
  3. Step 3: Divisible by 5? 378 does not end in 0 or 5. No ✗
  4. Step 4: Divisible by 7? 37 - 2(8) = 37 - 16 = 21. Since 21÷7 = 3, yes ✓
  5. Step 5: 378 is divisible by 2, 3, 6, 7, 9. Prime factorization: 2 × 3³ × 7.

Frequently Asked Questions

How do I know if a number is divisible by 2?

A number is divisible by 2 if it is even, meaning it ends in 0, 2, 4, 6, or 8. Simply check the last digit.

What is the divisibility rule for 3?

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 852: 8+5+2 = 15, and 15÷3 = 5, so 852 is divisible by 3.

How do I test divisibility by 7?

Double the last digit and subtract it from the rest of the number. If the result is divisible by 7, so is the original. Repeat if needed. Example: 371 → 37 - 2(1) = 35, which is divisible by 7.

What is the rule for divisibility by 11?

Find the alternating sum of digits (from right to left): add and subtract digits alternately. If the result is 0 or divisible by 11, the number is divisible by 11. Example: 121: 1 - 2 + 1 = 0. ✓

What is the divisibility rule for 9?

A number is divisible by 9 if the sum of its digits is divisible by 9. This is similar to the rule for 3. For example, 729: 7+2+9 = 18, and 18÷9 = 2, so 729 is divisible by 9.

How do I test divisibility by 12?

A number is divisible by 12 if it is divisible by both 3 AND 4. Check divisibility by 3 (digit sum divisible by 3) and by 4 (last two digits divisible by 4) separately.

What is the rule for divisibility by 6?

A number is divisible by 6 if it is divisible by both 2 and 3. It must be even AND its digit sum must be divisible by 3.

Are there divisibility rules for numbers greater than 12?

Yes, there are rules for larger numbers, but they become more complex. For 13: multiply last digit by 4 and add to the rest. For 17: multiply last digit by 5 and subtract from the rest. For 19: multiply last digit by 2 and add to the rest.