Divisibility Rules

Mental Math · Axiom Academy

Master quick mental tests to determine if a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10, or 11—no calculator needed! This is the simplest rule! You only need to look at the ones place. If the last digit is even, the entire number is divisible by 2. Add up all the digits in the number. If that sum is divisible by 3, then the original number is divisible by 3. You can repeat the process on the sum if needed! Ignore everything except the last two digits. If those two digits form a number that's divisible by 4 (or if the last two digits are 00), then the whole number is divisible by 4. Another super simple rule! Just look at the ones place. If it's 0 or 5, the number is divisible by 5. Since 6 = 2 × 3, a number must pass both tests. Check if the last digit is even (rule for 2), then check if the sum of digits is divisible by 3 (rule for 3). Both must be true! Similar to the rule for 4, but now we look at the last THREE digits. If those three digits form a number divisible by 8 (or if they're 000), then the whole number is divisible by 8. This is just like the rule for 3, but stricter! Add up all the digits. If that sum is divisible by 9, then the original number is divisible by 9. You can repeat the digit sum if needed. The easiest rule of all! If a number ends in 0, it's divisible by 10. That's it!

This is the written version of the interactive lesson above. See the full Mental Math course.