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Quizzes > Mathematics > Basic Math & Arithmetic

Take the Ultimate Divisibility Rules Quiz!

Ace Your Divisibility Tests - Practice Rules for 5, 3 & Beyond

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
paper art illustration with digits and division signs on sky blue for a quiz on divisibility rules for 3 5 11 and more

Welcome to our free divisibility test quiz, specially designed to challenge students, educators, and math enthusiasts alike! Dive into engaging tests for divisibility covering rules for 3, 5, 11, and more. In this quick assessment, you'll explore real divisibility test examples, discover the simple yet powerful divisibility test for 5, and solidify your divisibility rules practice. Perfect for anyone looking to reinforce number theory fundamentals or prep for classroom success. Ready for more? After you ace this quiz, deepen your skills with our division math quiz or sharpen your fundamentals in the Multiplication and Division Quiz . Take the quiz now and see how you measure up!

Which of the following numbers is divisible by 2?
551
246
379
135
A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). The last digit of 246 is 6, which is even, so 246 is divisible by 2. Other numbers here end in odd digits and therefore are not divisible by 2. Learn more about the rule for 2.
Which of the following numbers is divisible by 3?
125
123
124
127
A number is divisible by 3 if the sum of its digits is a multiple of 3. For 123, the sum is 1 + 2 + 3 = 6, which is divisible by 3, so 123 is divisible by 3. The other sums are not multiples of 3. See the rule for 3.
Which of the following numbers is divisible by 5?
370
372
378
379
A number is divisible by 5 if its last digit is either 0 or 5. The last digit of 370 is 0, so it meets the rule for divisibility by 5. None of the other options end in 0 or 5. Read more about divisibility by 5.
Which of the following numbers is divisible by 9?
891
892
895
896
A number is divisible by 9 if the sum of its digits is a multiple of 9. For 891, the sum is 8 + 9 + 1 = 18, which is divisible by 9. The other sums are not multiples of 9. Learn about the rule for 9.
Which of the following numbers is divisible by 4?
312
313
315
314
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. In 312, the last two digits are 12, and 12 ÷ 4 = 3 with no remainder. None of the other last-two-digit pairs divide evenly by 4. See the divisibility rule for 4.
Which of the following numbers is divisible by 6?
117
118
115
114
A number is divisible by 6 if it is divisible by both 2 and 3. For 114, the last digit is 4 (even), so it's divisible by 2, and the sum of its digits is 1+1+4=6, divisible by 3. Therefore 114 is divisible by 6. Read the rule for 6.
Which of the following numbers is divisible by 7 using the doubling-the-last-digit method?
204
203
206
205
In the 7-rule, you double the last digit and subtract it from the rest of the number. For 203: double 3 is 6, then 20 ? 6 = 14, which is divisible by 7. That means 203 is divisible by 7. Learn more about the rule for 7.
Which of the following numbers is divisible by 8?
457
458
459
456
A number is divisible by 8 if the last three digits form a number that is divisible by 8. Here, 456 ÷ 8 = 57 with no remainder, so 456 is divisible by 8. The other last-three-digit values do not divide evenly by 8. See the divisibility rule for 8.
Which of the following numbers is divisible by 11?
2757
2728
2749
2738
A number is divisible by 11 if the alternating sum of its digits is a multiple of 11. For 2728: (2 ? 7 + 2 ? 8) = ?11, which is divisible by 11, so 2728 is divisible by 11. The others do not give a multiple of 11. Learn the rule for 11.
Which of the following numbers is divisible by 12?
195
194
193
192
A number is divisible by 12 if it is divisible by both 3 and 4. For 192, the digit sum is 1+9+2=12 (divisible by 3) and the last two digits, 92, ÷ 4 = 23 with no remainder. Therefore 192 is divisible by 12. See the rule for 12.
Which of the following numbers is divisible by 14?
199
196
197
198
A number is divisible by 14 if it is divisible by both 2 and 7. For 196, the last digit is 6 (even), so it's divisible by 2, and using the 7-rule: double 6 is 12, 19 ? 12 = 7 (divisible by 7). Hence 196 is divisible by 14. Learn more about divisibility by 14.
True or False: The number 123456 is divisible by 33.
False
True
A number is divisible by 33 if it is divisible by both 3 and 11. For 123456 the sum of digits is 1+2+3+4+5+6 = 21, which is divisible by 3, but the alternating sum for 11 is (1 ? 2 + 3 ? 4 + 5 ? 6) = -3, which is not a multiple of 11. Therefore, 123456 is not divisible by 33. Review divisibility rules for 3 and 11.
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Study Outcomes

  1. Understand key divisibility rules -

    Confidently grasp the criteria for determining whether a number is divisible by 2, 3, 5, 11, and more, enhancing your divisibility test foundation.

  2. Apply practical divisibility tests -

    Use quick mental shortcuts and tests for divisibility to efficiently check number factors without extensive calculations.

  3. Differentiate tests for divisibility -

    Recognize and articulate how rules vary for specific divisors, including the divisibility test for 5 versus the rule for 11.

  4. Analyze numerical patterns for divisibility -

    Examine digit sums, alternating sums, and other patterns in divisibility rules practice to solve problems more effectively.

  5. Evaluate your divisibility skills -

    Assess your performance through the quiz's feedback, identifying strengths and areas needing additional divisibility test practice.

  6. Master advanced tests for divisibility -

    Develop expertise in less common divisibility rules, broadening your ability to test larger and more complex numbers seamlessly.

Cheat Sheet

  1. Even and "High Five" Rule for 2 and 5 -

    Numbers ending in an even digit are divisible by 2, while those ending in 0 or 5 pass the divisibility test for 5 (University of Cambridge). The mnemonic "Even Steven" helps you spot evens instantly, and "High Five" reminds you of the 5-rule. Practice these simple tests for divisibility to speed up your calculations.

  2. Digital Sum Test for 3 and 9 -

    The digital sum method states that a number is divisible by 3 if the sum of its digits is divisible by 3, and by 9 if that sum divides by 9 (MIT OpenCourseWare). For example, 4+5+7=16, and since 16 is not a multiple of 3, 457 isn't divisible by 3. Integrate this divisibility test with your regular divisibility rules practice to quickly spot factors.

  3. Alternating Sum Rule for 11 -

    The divisibility test for 11 uses the alternating sum of digits: subtract the sum of even-positioned digits from the sum of odd-positioned digits - if the result is 0 or a multiple of 11, the number is divisible by 11 (Britannica). For instance, for 6273: (6+7)−(2+3)=8, so it fails the test; but 5831: (5+3)−(8+1)=−1, showing it's not divisible by 11 either. Mastering this rule boosts your overall divisibility tests toolkit.

  4. "Double and Subtract" Trick for 7 -

    To test divisibility by 7, double the last digit and subtract it from the remaining truncated number; if the result is divisible by 7, so is the original number (University of Oxford). For example, 658: 65−2×8=49, which is 7×7, confirming 658 is divisible by 7. Regularly applying this test enhances your divisibility rules practice for more complex primes.

  5. Composite Checks and Prime Factor Insights -

    Combining basic divisibility tests helps factor larger numbers efficiently; for instance, 420 is divisible by 2, 3, 5, and 7, yielding its prime factors 2×2×3×5×7 (Stanford Mathematics). By sequentially applying the divisibility test for 2, then 3, then 5, and finally 7, you can break numbers down quickly. Use this structured approach in your divisibility rules practice to tackle number puzzles confidently.

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