Divisibility rules worksheet for students to practice identifying which numbers a given number is divisible by.

Let's solve each question step by step using the divisibility rules provided in the note at the bottom of the image.

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Divisibility Rules Recap:

1. 2: Last digit is even (0, 2, 4, 6, 8)
2. 3: Sum of digits divisible by 3
3. 4: Last two digits form a number divisible by 4
4. 5: Last digit is 0 or 5
5. 6: Divisible by both 2 and 3
6. 9: Sum of digits divisible by 9

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Now, let’s go through each question:

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1. 455 is divisible by _________.

- Last digit = 5 → divisible by 5
- Sum of digits: 4 + 5 + 5 = 14 → not divisible by 3 → not by 3 or 9
- Last digit odd → not divisible by 2 → not by 4, 6
- Last two digits: 55 → 55 ÷ 4 = 13.75 → not divisible by 4

✔ Answer: 5

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2. 3939 is divisible by _________.

- Last digit = 9 → odd → not divisible by 2, 4, 6
- Last digit ≠ 0 or 5 → not divisible by 5
- Sum of digits: 3 + 9 + 3 + 9 = 24 → 24 ÷ 3 = 8 → divisible by 3
- 24 ÷ 9 = 2.66… → not divisible by 9

✔ Answer: 3

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3. 2432 is divisible by _________.

- Last digit = 2 → even → divisible by 2
- Sum of digits: 2 + 4 + 3 + 2 = 11 → not divisible by 3 → not by 3, 6, 9
- Last two digits: 32 → 32 ÷ 4 = 8 → divisible by 4
- Not ending in 0 or 5 → not divisible by 5
- Since divisible by 2 and 4, but not by 3 → not by 6

So divisible by 2 and 4

But the blank asks for one number? Let's see — probably expect 2 or 4?

Wait — check if it's divisible by any of the numbers listed.

It is divisible by 2 and 4, so we can write either.

But since it says "divisible by" and gives one blank, likely expecting 2 or 4.

But let’s check: Is it divisible by 6? No — sum is 11 → not divisible by 3 → no.

So only 2 and 4

But which to write? Probably just one.

But maybe they want all possible?

Looking at format: Sample says “divisible by 5” — single number.

But some questions have multiple blanks.

For this one, only one blank → pick one valid.

But perhaps best to write 4, because it’s divisible by 4 ⇒ also by 2.

But the question doesn’t say "all", just "divisible by".

So any correct answer is acceptable.

Let’s choose 4 (since 32 is divisible by 4)

But actually, 2 is simpler.

But let's see later ones — maybe better to list what fits.

Wait: Let’s check 2432:
- Ends with 2 → divisible by 2 ✔
- Last two digits: 32 → divisible by 4 ✔
- Sum = 11 → not divisible by 3 → not by 3, 6, 9
- Not ending in 0 or 5 → not by 5

So divisible by 2 and 4

But since only one blank, we must pick one.

But perhaps the expected answer is 2 or 4.

Let’s assume they want the largest applicable? Or just one.

But in such problems, often they accept any correct divisor.

But to be safe, let's look at pattern.

But for now, I’ll write 2 (as it’s basic).

Wait — better: 4 is stronger.

But let’s keep going.

Actually, let’s do it properly.

Wait — 2432 ÷ 2 = 1216 → yes
2432 ÷ 4 = 608 → yes
2432 ÷ 8 = 304 → but 8 not in list.

So divisible by 2 and 4

Since only one blank, perhaps they expect 4? But not sure.

But wait — Question 7 has two blanks.

So maybe here, only one.

But let’s assume we can write 4.

But actually, 2 is sufficient.

But let's see the next.

Alternatively, perhaps they expect 2.

But I think 4 is fine.

Wait — let’s check 2432 ÷ 4 = 608 → yes.

But 2 is also correct.

But let’s move on and come back.

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4. 6273 is divisible by _________.

- Last digit = 3 → odd → not divisible by 2, 4, 6
- Last digit ≠ 0 or 5 → not divisible by 5
- Sum of digits: 6 + 2 + 7 + 3 = 18 → 18 ÷ 3 = 6 → divisible by 3
- 18 ÷ 9 = 2 → divisible by 9

So divisible by 3 and 9

Only one blank → write one of them.

But which?

Probably 3 or 9

But 9 is stronger.

But both are correct.

But let’s see: 6273 ÷ 9 = 700 - ? Let's check:

9 × 697 = ?

Better: 6+2+7+3=18 → divisible by 9 → yes.

So divisible by 9

Also by 3.

But since 9 implies 3, perhaps write 9

But again, only one blank.

We can write 9

But let's confirm: 6273 ÷ 9 = 697 → 9×697 = 6273?
9×700 = 6300 → 6300 - 9×3 = 6300 - 27 = 6273 → yes.

So yes.

✔ Answer: 9

(Or 3, but 9 is better)

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5. If a number is divisible by 4, then it is also divisible by _________.

- A number divisible by 4 means last two digits divisible by 4.
- But divisible by 4 ⇒ divisible by 2 (since 4 is multiple of 2)

Example: 12 → divisible by 4 → also by 2

So 2

✔ Answer: 2

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6. 935050 is divisible by _________.

- Last digit = 0 → divisible by 2 and 5
- Also ends with 0 → divisible by 10 → so divisible by 2 and 5
- Sum of digits: 9 + 3 + 5 + 0 + 5 + 0 = 22 → 22 not divisible by 3 → not by 3, 6, 9
- Last two digits: 50 → 50 ÷ 4 = 12.5 → not divisible by 4

So divisible by 2 and 5

But only one blank → write one.

But which?

The question says "divisible by" — could be 2 or 5.

But since it ends with 0 → divisible by 10 → so definitely divisible by 5

Also by 2.

But perhaps they expect 5 or 2

But let’s see: 5 is more specific.

But 2 is fine too.

But wait — check divisibility by 5: last digit 0 → yes → divisible by 5

Also by 2.

But since only one blank, we can write 5

But actually, 5 is a good choice.

Alternatively, 2

But let’s see — perhaps they expect 5 because it ends in 0.

But both are correct.

But looking at context — maybe 5 is expected.

But wait — 935050 → ends with 0 → divisible by 10, so by 2 and 5

But only one blank.

Perhaps write 5 or 2

But let’s move on.

Wait — Question 7 has two blanks.

So for this, one blank → pick one.

I’ll go with 5

But let’s double-check.

Is it divisible by 4? Last two digits: 50 → 50 ÷ 4 = 12.5 → no

By 3? Sum = 22 → no

By 9? 22 → no

So only 2 and 5

So answer: 5 or 2

But since it ends in 0, 5 is a strong candidate.

But 2 is also correct.

But perhaps the intended answer is 5

Wait — Question 1 had 455 → divisible by 5 → ends in 5

This ends in 0 → so divisible by 5

So likely 5

✔ Answer: 5

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7. 92454 is divisible by _________ and _________.

Two blanks.

Check:

- Last digit = 4 → even → divisible by 2
- Sum of digits: 9 + 2 + 4 + 5 + 4 = 24 → 24 ÷ 3 = 8 → divisible by 3
- So divisible by 2 and 3 → therefore divisible by 6
- Check 4: last two digits = 54 → 54 ÷ 4 = 13.5 → not divisible by 4
- Last digit ≠ 0 or 5 → not by 5
- Sum = 24 → divisible by 3, but 24 ÷ 9 = 2.66 → not by 9

So divisible by 2, 3, 6

But the question says "divisible by ___ and ___"

So likely 2 and 3, or 2 and 6, or 3 and 6

But since divisible by 2 and 3 → automatically divisible by 6

But the rule says: divisible by 6 if divisible by 2 and 3

So it is divisible by 2 and 3, and hence by 6

But the question wants two numbers.

Best to write 2 and 3 or 2 and 6

But 6 is a consequence.

But perhaps they expect 2 and 6

But let’s see: the number is divisible by 6?

Yes — since divisible by 2 and 3.

So we can write 2 and 6

Or 3 and 6

But most logical: 2 and 3 → because that's why it's divisible by 6

But since it asks for divisors, and 6 is one, maybe write 2 and 6

But let’s see.

Alternatively, 2 and 3 is safer.

But the rule says: divisible by 6 if divisible by 2 and 3.

So both are true.

But the number is divisible by 2, 3, and 6

So for two blanks, we can write 2 and 6, or 3 and 6, or 2 and 3

But likely they expect 2 and 3 as base, or 2 and 6

But let’s check: 92454 ÷ 6 = ?

92454 ÷ 2 = 46227
46227 ÷ 3 = 15409 → so yes, divisible by 6

So yes.

But which pair?

Since the problem says "divisible by ___ and ___", and 6 is a divisor, perhaps write 2 and 6

But 2 and 3 is also correct.

But 2 and 6 might be better.

Wait — Question 8 says divisible by 2 and ___ → so expects another

So here, two blanks — could be 2 and 6, or 3 and 6, or 2 and 3

But since it’s divisible by 2 and 3, and 6, any combination.

But 2 and 3 is fundamental.

But let’s see: Question 8 has “divisible by 2 and ___” → so likely expects 6

Similarly, here, maybe 2 and 6

But 92454 is divisible by 2 and 6? Yes.

But also by 3.

But 6 is stronger.

But I think 2 and 6 is acceptable.

But let’s go with 2 and 6

Wait — is it divisible by 4? Last two digits: 54 → 54 ÷ 4 = 13.5 → no

By 9? Sum = 24 → 24 ÷ 9 = 2.66 → no

So only 2, 3, 6

So possible pairs: 2 & 3, 2 & 6, 3 & 6

But since 6 is derived from 2 and 3, perhaps write 2 and 3

But let’s see what is expected.

In many such worksheets, they ask for 2 and 3 when divisible by 6.

But here, since it says "divisible by ___ and ___", and 6 is a divisor, maybe 2 and 6

But I think 2 and 3 is better.

But let’s look at Question 8:

8. 73384 is divisible by 2 and _________.

Let’s solve that first.

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8. 73384 is divisible by 2 and _________.

- Last digit = 4 → even → divisible by 2
- Last two digits = 84 → 84 ÷ 4 = 21 → divisible by 4
- Sum of digits: 7 + 3 + 3 + 8 + 4 = 25 → not divisible by 3 → not by 3, 6, 9
- Not ending in 0 or 5 → not by 5

So divisible by 2 and 4

So blank should be 4

✔ Answer: 4

Back to 7: 92454

Divisible by 2 and 3, and thus by 6

But only 2 and 3 are required to deduce 6

But the number is divisible by 2 and 6, or 3 and 6

But since 6 is a divisor, and the number is divisible by 6, we can say it’s divisible by 2 and 6

But 2 and 3 is also correct.

But to match style, perhaps 2 and 6

But 6 is not independent — it depends on 2 and 3.

But since the number is divisible by 6, and by 2, we can say 2 and 6

Similarly, 3 and 6

But let’s see: Question 13 says: "A number divisible by 2 and 3 is divisible by ___" → answer is 6

So in reverse, if divisible by 2 and 3, then by 6.

So for 7, since divisible by 2 and 3 → divisible by 6

So the two divisors could be 2 and 3

I think 2 and 3 is best.

✔ Answer: 2 and 3

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9. A number which is divisible by 10 is also divisible by _________.

- Divisible by 10 → ends with 0 → so divisible by 2 and 5
- So also divisible by 2 and 5

But the blank is singular → write one?

But likely 2 or 5

But since divisible by 10 → divisible by 2 and 5

But the question says "also divisible by" → one number

But which?

Both are true.

But perhaps they expect 5, or 2

But common answer is 5

But 2 is also correct.

But let’s think: divisible by 10 → divisible by 2 and 5

But the question says "by _________" → one blank

So write one.

But which?

But actually, 5 is more specific.

But 2 is also.

But perhaps 5

Wait — Question 1 was 455 → divisible by 5

Here, divisible by 10 → so divisible by 5

So likely 5

But 2 is also correct.

But perhaps 5

But let’s see: divisible by 10 → always divisible by 2 and 5

So answer could be 2 or 5

But since 10 is multiple of 5, and 5 is a factor, perhaps 5

But 2 is also.

But I think 5 is fine.

But let’s check standard: usually, they say divisible by 2 and 5.

But here, one blank.

Perhaps 5

But I think 2 is equally valid.

But let’s see: if a number is divisible by 10, it is divisible by 5

Yes.

So ✔ Answer: 5

(Or 2 — but 5 is better)

But let’s go with 5

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10. Give one number which is divisible by 6 _________.

Any number divisible by both 2 and 3.

For example: 6, 12, 18, etc.

Simplest: 6

✔ Answer: 6 (or any multiple of 6)

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11. 9936 is divisible by _________.

- Last digit = 6 → even → divisible by 2
- Last two digits = 36 → 36 ÷ 4 = 9 → divisible by 4
- Sum of digits: 9 + 9 + 3 + 6 = 27 → 27 ÷ 3 = 9 → divisible by 3
- 27 ÷ 9 = 3 → divisible by 9
- So divisible by 2, 3, 4, 6, 9

But only one blank → write one.

Which one?

But 9 is strong.

But 6 is also.

But since sum is 27 → divisible by 9 → so divisible by 9

Also by 3.

But 9 is better.

Also divisible by 4? Yes — 36 ÷ 4 = 9 → yes

So divisible by 4

But 9 is a good choice.

But let’s see: divisible by 6? Yes — since divisible by 2 and 3

But 9 is higher.

But any correct one.

But perhaps they expect 9

But let’s check: 9936 ÷ 9 = ?

9 × 1104 = 9936?
9 × 1100 = 9900, 9 × 4 = 36 → 9900 + 36 = 9936 → yes

So divisible by 9

✔ Answer: 9

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12. 899991 is divisible by _________ and _________.

Two blanks.

- Last digit = 1 → odd → not divisible by 2, 4, 6
- Last digit ≠ 0 or 5 → not divisible by 5
- Sum of digits: 8 + 9 + 9 + 9 + 9 + 1 = 45 → 45 ÷ 3 = 15 → divisible by 3
- 45 ÷ 9 = 5 → divisible by 9

So divisible by 3 and 9

✔ Answer: 3 and 9

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13. A number which is divisible by 2 and 3, is divisible by _________.

From rule: divisible by 6

✔ Answer: 6

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14. If the last digit of a number is 0 then it is divisible by ________ and _________.

- Last digit 0 → divisible by 2 and 5
- Because 0 is even → divisible by 2
- And ends with 0 → divisible by 5

✔ Answer: 2 and 5

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15. 1916 is divisible by 4. State true or false _________.

- Last two digits = 16 → 16 ÷ 4 = 4 → divisible by 4

So true

✔ Answer: True

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Now, let’s compile all answers:

1. 455 is divisible by 5
2. 3939 is divisible by 3
3. 2432 is divisible by 2 (or 4) → but let’s pick 4 (since last two digits 32 divisible by 4)
But earlier I said 2 — but 4 is better.

Wait: 2432 → last two digits 32 → 32 ÷ 4 = 8 → divisible by 4

So divisible by 4

Also by 2.

But since 4 is stronger, and 4 is in the list, write 4

✔ Answer: 4

4. 6273 is divisible by 9 (sum = 18 → divisible by 9)
5. If divisible by 4, then also divisible by 2
6. 935050 is divisible by 5 (ends in 0)
7. 92454 is divisible by 2 and 3
8. 73384 is divisible by 2 and 4
9. A number divisible by 10 is also divisible by 5
10. One number divisible by 6: 6
11. 9936 is divisible by 9
12. 899991 is divisible by 3 and 9
13. Divisible by 2 and 3 → divisible by 6
14. Last digit 0 → divisible by 2 and 5
15. 1916 divisible by 4 → True

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Final Answers:

1. 5
2. 3
3. 4
4. 9
5. 2
6. 5
7. 2 and 3
8. 4
9. 5
10. 6 (or 12, 18, etc.)
11. 9
12. 3 and 9
13. 6
14. 2 and 5
15. True

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✔ All solved!