Grade 6 Math · Topic 31

Divisibility Rules

Divisibility rules are shortcuts that let you tell whether one whole number divides evenly into another — without doing the actual division. They are huge time-savers for factoring, simplifying fractions, and finding GCFs and LCMs.

Lesson alignment: 6.NS.B.4 (divisibility supports GCF and LCM) · Take your time. You can return to this lesson whenever you need it.

Explore visually

Test a divisibility rule

Choose a divisor and see the exact digit test that proves whether the number divides evenly.

Think first: Which digit test fits the divisor you chose, and what result do you predict?

Ready? Reveal the model and try your prediction

Swipe horizontally to see the full diagram.

Turn on JavaScript to adjust this model. The examples and practice below work without it.

Follow the worked examples

Read each step, then cover the explanation and see if you can explain why it works.

Worked example 1

Is 738 divisible by 3?

Add the digits: 7+3+8 = 18. Since 18 ÷ 3 = 6, yes — 738 is divisible by 3.

Answer: Yes

Worked example 2

Is 1,260 divisible by 9?

Digit sum: 1+2+6+0 = 9. Since 9 ÷ 9 = 1, yes — 1,260 is divisible by 9.

Answer: Yes

Try a few on your own

Work these on paper first. Open “Check” when you are ready to compare your answer.

  1. Is 456 divisible by 2? ⇒
    Check

    Yes

  2. Is 837 divisible by 3? ⇒
    Check

    Yes

  3. Is 624 divisible by 4? ⇒
    Check

    Yes

  4. Is 245 divisible by 5? ⇒
    Check

    Yes

  5. Is 378 divisible by 6? ⇒
    Check

    Yes

  6. Is 5,481 divisible by 9? ⇒
    Check

    Yes

  7. Is 7,320 divisible by 10? ⇒
    Check

    Yes

  8. Is 924 divisible by 6? ⇒
    Check

    Yes

Try this situation 1

Mrs. Lee has 144 cookies. Can she share them equally among 9 students?

Show a worked solution

Answer: Yes.

Digit sum of 144 is 1+4+4 = 9, divisible by 9. So 144 ÷ 9 = 16.

Try this situation 2

A theater has 375 seats. Can they be split equally into rows of 6?

Show a worked solution

Answer: No.

Start by writing the calculation clearly: 375 is not even (last digit 5), so it is not divisible by 2, and therefore not by 6.

Fresh questions · saved on this device

Practice this skill

10 question pool

Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.

Choose a session length

Your practice results stay in this browser and appear in the course progress report.

Check what you learned

Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.

1. Which of these numbers is divisible by 2 but NOT by 4?

2. A librarian has 312 books to arrange. She can organize them into rows with 6 books each. How do you know 312 is divisible by 6?

3. Which number is divisible by 4?

4. Which number below is divisible by 9?

5. A factory packages 450 items. Using divisibility rules, decide which size package can use all items with none left over.

Practice and finish

Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.

Open the practice quiz

Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.

More Grade 6 resources

Use these free materials if you want another explanation, extra paper practice, or a broader review.

Browse free Grade 6 topic lessons ↗Print Grade 6 worksheets ↗Review Grade 6 flashcards ↗Open the formula review ↗Try the Factors, Multiples & Percents quiz ↗Try a full practice test ↗