Divisibility Tests

Did you know one divisibility rule is really just two simpler rules working together? These quizzes on whole-number divisibility show how stacking the tests lets you check tricky divisors fast.

Testing Whole Numbers for Divisibility

You will pick the number that divides evenly or judge true or false statements, with prompts like which number is divisible by 6, or whether 588 is divisible by 7. The first quiz covers the everyday divisors, and the second steps up to harder ones, including divisible-by-all-except questions with numbers like 11 and 13.

Rather than dividing the long way, you lean on quick tests and combine them. Checking 588 for 6, for instance, just means confirming it passes the tests for both 2 and 3. These sets run from intermediate to advanced. Treating each test as a building block is what makes the harder divisors feel manageable.

Did You Know?

The rule for 6 is two rules in one. A number is divisible by 6 only if it passes the test for 2 and the test for 3, so 588 qualifies because it is even and its digits add to a multiple of 3.

You can chain rules the same way for other divisors. A number divisible by both 3 and 4 is automatically divisible by 12, which saves you from ever testing 12 directly.

How the Quizzes Work

Each quiz is brief, about five minutes, and you can replay both whenever you want the combined tests to feel natural. Once you start seeing divisibility as a set of stackable shortcuts, even large numbers stop being intimidating. The same approach is how you start checking whether a number is prime, by ruling out small divisors one at a time. Ready to put the rules together? Jump into the free interactive math quizzes and start checking.

3. Divisibility Rules 1

This quiz puts the divisibility rules to work across 12 questions, where you pick the number that divides evenly or judge true-or-false statements. You will face prompts like Which number is divisible by 6? or The number 588 is divisible by 7., so it rewards knowing the shortcuts rather than doing long division. A connection worth spotting is that the rule for 6 is really two rules in one: a number works only if it passes both the test for 2 and the test for 3. Stacking simple rules like that lets you check trickier divisors fast. Recommended level: intermediate.

score: 0% (everyone)

12 questions

4. Divisibility Rules 2

Building on the basics, this quiz runs 11 questions on tougher divisors, including some "divisible by all of these except" prompts. You might read Which number is divisible by 11? or The number 286 is divisible by 13., which pushes you past the easy single-digit tests. The rule for 11 is the surprising one: you add and subtract the digits in an alternating pattern, and if that result divides by 11, so does the whole number. It feels like a magic trick the first time it works out. Recommended level: intermediate to advanced.

score: 0% (everyone)

11 questions