Divisibility Patterns Quiz: Find the Missing Number (2–10)

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| Questions: 20 | Updated: Dec 15, 2025
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1) 9, 18, 27, 36, 45 → Which rules fit all these numbers?

Explanation

Digit sums are 9, 9, 9, 9, 9 → divisible by 9, hence also by 3. They are not all multiples of 6, 12, or 15.

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Divisibility Patterns Quiz: Find The Missing Number (210) - Quiz

Ready to put your number sense to the test? This quiz helps you explore divisibility rules from 2 to 10 and use them to fill in missing numbers. You’ll spot patterns, apply quick checks, and uncover the logic behind each rule. It’s a fun way to sharpen your math skills... see moreand see how well you can reason through number puzzles. Jump in and give it a try! see less

2) 16, 24, 32, 40, __ → All divisible by 8.

Explanation

Increase by 8: 40 + 8 = 48, and 48 ÷ 8 = 6 (no remainder).

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3) 18, 27, 36, 45, 54 → All divisible by 9.

Explanation

Digit sums are 9 for each term (1+8, 2+7, …), so each divides by 9 exactly.

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4) 15, 30, 45, 60, 75 → Which rules fit all these numbers?

Explanation

They all end in 0 or 5 (÷5) and have digit sums divisible by 3 (÷3). Therefore each is a multiple of 15 as well.

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

Explanation

Add 9 each step: 45 + 9 = 54. Also 5+4=9 → 54 ÷ 9 = 6.

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6) Which sequences have all numbers divisible by 4?

Explanation

A and B consist only of multiples of 4. C has 6 and 18 (not ÷4), D has 10 and 30 (not ÷4), E has none ÷4.

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7) 12, 24, 36, 48, __ → All divisible by 6.

Explanation

Increase by 12: 48 + 12 = 60. Also 60 ÷ 6 = 10 (no remainder).

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8) 8, 16, 24, 32, 40 → All divisible by 8.

Explanation

Each term is 8×(1,2,3,4,5), so they all divide by 8 with no remainder.

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9) 14, 21, 28, __, 42 → Multiples of 7.

Explanation

They are 7×2, 7×3, 7×4, 7×5, 7×6. Missing is 7×5 = 35.

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10) 20, 30, 40, __, 60 → All divisible by 10.

Explanation

Add 10 each step: 40 + 10 = 50. 50 ends in 0, so 50 ÷ 10 = 5 exactly.

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11) 8, 16, 24, 32, __ → All divisible by 8.

Explanation

Each term increases by 8: 8→16(+8)→24(+8)→32(+8)→40(+8). Since 40 ÷ 8 = 5 (no remainder), 40 fits the rule.

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12) 16, 22, 32, 40, 48 → Which number does NOT belong?

Explanation

All but 22 are divisible by 8: 16 ÷ 8 = 2, 32 ÷ 8 = 4, 40 ÷ 8 = 5, 48 ÷ 8 = 6. But 22 ÷ 8 = 2.75 (not an integer).

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13) 35, 42, 49, __, 63 → Multiples of 7.

Explanation

Add 7 each time: 49 + 7 = 56. Also 56 = 7 × 8.

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14) 6, 12, 18, 24, 30 → All divisible by 6.

Explanation

Each term is even (÷2) and has digit sum divisible by 3 (÷3). Numbers divisible by both 2 and 3 are divisible by 6.

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15) 10, 20, 30, 40, 50 → Which rules fit all these numbers?

Explanation

All end in 0, so divisible by 2, 5, and 10. Not all digit sums are multiples of 3 or 9.

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16) 4, 12, 20, __, 36 → All divisible by 4.

Explanation

The sequence increases by 8: 4→12(+8)→20(+8)→28(+8)→36(+8). 28 ÷ 4 = 7 with no remainder.

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17) 18, 27, 36, 45, __ → All divisible by 9.

Explanation

Add 9 each time: 45 + 9 = 54. Also 5+4=9, so 54 is divisible by 9 (54 ÷ 9 = 6).

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18) 25, 50, 75, 100, __ → The next number must be divisible by 4.

Explanation

These are multiples of 25 (25k). 25 ÷ 4 is not an integer, so the pattern is divisibility by 25, not by 4. The next term 125 is not divisible by 4.

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19) 14, 28, 42, 56, 70 → Which rules fit all these numbers?

Explanation

All are even, so divisible by 2. They are 7×(2,4,6,8,10), so divisible by 7. Not all end in 0 or 5 (so not 5 or 10), and their digit sums are not always multiples of 9.

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20) 15, 30, 45, __, 75 → All divisible by 15.

Explanation

Multiples of 15 increase by 15: 45 + 15 = 60. Also, 60 ends with 0 and 6+0=6 is divisible by 3, so 60 ÷ 15 = 4 (no remainder).

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9, 18, 27, 36, 45 → Which rules fit all these numbers?
16, 24, 32, 40, __ → All divisible by 8.
18, 27, 36, 45, 54 → All divisible by 9.
15, 30, 45, 60, 75 → Which rules fit all these numbers?
27, 36, 45, __, 63 → All divisible by 9.
Which sequences have all numbers divisible by 4?
12, 24, 36, 48, __ → All divisible by 6.
8, 16, 24, 32, 40 → All divisible by 8.
14, 21, 28, __, 42 → Multiples of 7.
20, 30, 40, __, 60 → All divisible by 10.
8, 16, 24, 32, __ → All divisible by 8.
16, 22, 32, 40, 48 → Which number does NOT belong?
35, 42, 49, __, 63 → Multiples of 7.
6, 12, 18, 24, 30 → All divisible by 6.
10, 20, 30, 40, 50 → Which rules fit all these numbers?
4, 12, 20, __, 36 → All divisible by 4.
18, 27, 36, 45, __ → All divisible by 9.
25, 50, 75, 100, __ → The next number must be divisible by 4.
14, 28, 42, 56, 70 → Which rules fit all these numbers?
15, 30, 45, __, 75 → All divisible by 15.
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