Divisibility Challenge Quiz: Master Rules from 2–10

  • 4th Grade
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| Questions: 20 | Updated: Dec 16, 2025
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1) 4, 8, 12, 16, __ → All divisible by 4.

Explanation

Each number increases by 4. 16 + 4 = 20. Check → 20 ÷ 4 = 5, no remainder.

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About This Quiz
Divisibility Challenge Quiz: Master Rules From 210 - Quiz

Think you’ve mastered divisibility rules from 2 to 10? This quiz puts your skills to the test with quick checks, clever patterns, and number puzzles that keep you on your toes. You’ll practice spotting what divides cleanly, find missing values, and sharpen your ability to reason through problems using simple... see morerules. Dive in and see how confidently you can handle every divisibility trick coming your way!
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2) 15, 30, 45, 60, __ → All divisible by 15.

Explanation

Each step adds 15. 60 + 15 = 75. Ends in 5 → divisible by 5. Digit sum = 7 + 5 = 12 → divisible by 3 → also divisible by 15.

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3) 10, 20, 30, 40, 50 → Which rules fit all these numbers?

Explanation

All end in 0 → even (÷2), end in 0/5 (÷5), and since both true → divisible by 10.

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4) 32, 48, 64, 80 → All are divisible by 8.

Explanation

All have no remainder → all divisible by 8.

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5) 27, 36, 45, __, 63 → All divisible by 9.

Explanation

Sequence increases by 9 each time. 45 + 9 = 54. Sum of digits = 5 + 4 = 9 → divisible by 9.

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6) A number ends in 0. Which rule is true?

Explanation

Ends in 0 → even → ÷2; Ends in 0 → ÷5; Both → ÷10.

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7) 14, 28, 42, 56 → Which divisibility rules apply to all?

Explanation

All are even (÷2). Each = 7 × 2, 7 × 4, 7 × 6, 7 × 8 → ÷7 also.

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8) 18, 27, 36, 45, 54 → All divisible by 9.

Explanation

All have digit sums divisible by 9 → true.

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9) A number’s last two digits are 32. Which rule applies?

Explanation

If the last two digits form a number divisible by 4, the whole number is divisible by 4. 32 ÷ 4 = 8 → no remainder → rule applies.

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10) Which number is divisible by both 3 and 5?

Explanation

Ends in 0 → ÷5. Sum of digits = 3 → ÷3. Hence divisible by both → ÷15.

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11) Which numbers are divisible by 8?

Explanation

32 ÷ 8 = 4. 40 ÷ 8 = 5 . 48 ÷ 8 = 6 . 72 ÷ 8 = 9 . All divisible by 8.

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12) A number’s digits add to 18. Which rule is true?

Explanation

18 ÷ 9 = 2 → no remainder. If digit sum divides by 9, number itself divides by 9.

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13) Which number is divisible by 7 and 8?

Explanation

56 ÷ 7 = 8, 56 ÷ 8 = 7 → both whole → satisfies both.

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14) A number divisible by both 2 and 3 is automatically divisible by 6.

Explanation

LCM(2, 3) = 6. If number satisfies both rules, it must divide by 6.

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15) 5, 10, 15, 20, __ → All divisible by 5.

Explanation

Each increases by 5. Ends in 5 → rule for ÷5 satisfied.

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16) Which sequences contain only numbers divisible by 3?

Explanation

Digit sums → multiples of 3 → both first and second sequences work.

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17) Which number can be divided evenly by 2, 3, 4, and 5?

Explanation

60 ÷ 2 = 30, 60 ÷ 3 = 20, 60 ÷ 4 = 15, 60 ÷ 5 = 12 → all whole.

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18) A number ends in 0 and its digits add up to 9. It is divisible by 10 and 3.

Explanation

Ends in 0 → ÷10. Sum = 9 → ÷3. Both true → ÷30.

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19) A number that ends in 00 is divisible by 100.

Explanation

Ending in “00” means it divides evenly by 100 (100 × n). Example: 2300 ÷ 100 = 23 → whole number.

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20) Choose all true divisibility facts:

Explanation

9 → multiple of 3. Ends in 0 → ÷5. But 2 only ensures divisibility by 2, not 4 (e.g., 6 ÷ 4 ≠ whole)

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4, 8, 12, 16, __ → All divisible by 4.
15, 30, 45, 60, __ → All divisible by 15.
10, 20, 30, 40, 50 → Which rules fit all these numbers?
32, 48, 64, 80 → All are divisible by 8.
27, 36, 45, __, 63 → All divisible by 9.
A number ends in 0. Which rule is true?
14, 28, 42, 56 → Which divisibility rules apply to all?
18, 27, 36, 45, 54 → All divisible by 9.
A number’s last two digits are 32. Which rule applies?
Which number is divisible by both 3 and 5?
Which numbers are divisible by 8?
A number’s digits add to 18. Which rule is true?
Which number is divisible by 7 and 8?
A number divisible by both 2 and 3 is automatically divisible by 6.
5, 10, 15, 20, __ → All divisible by 5.
Which sequences contain only numbers divisible by 3?
Which number can be divided evenly by 2, 3, 4, and 5?
A number ends in 0 and its digits add up to 9. It is divisible by 10...
A number that ends in 00 is divisible by 100.
Choose all true divisibility facts:
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