Divisibility Rules worksheet with multiple-choice questions for practicing divisibility by 2, 3, 5, 6, 9, and 10.
Divisibility Rules worksheet with multiple-choice questions on divisibility by 2, 3, 5, 6, 9, and 10, featuring numbers from 7710 to 7769, from Learners' Planet.
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Step-by-step solution for: 301 Moved Permanently
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Show Answer Key & Explanations
Step-by-step solution for: 301 Moved Permanently
Let’s go through each problem one by one. We’ll check which numbers from the options divide evenly into the given number (no remainder).
We’ll use basic divisibility rules:
- Divisible by 2: Last digit is even (0, 2, 4, 6, 8)
- Divisible by 3: Sum of digits is divisible by 3
- Divisible by 5: Ends in 0 or 5
- Divisible by 6: Must be divisible by both 2 and 3
- Divisible by 9: Sum of digits is divisible by 9
- Divisible by 10: Ends in 0
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1) 7710
- Ends in 0 → divisible by 2, 5, 10
- Sum of digits: 7+7+1+0 = 15 → divisible by 3 → so also divisible by 6
→ So divisible by: 2, 3, 5, 6, 10 → Answer: A
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2) 7714
- Ends in 4 → divisible by 2
- Sum: 7+7+1+4 = 19 → not divisible by 3 → not by 6 or 9
- Doesn’t end in 0 or 5 → not by 5 or 10
→ Only divisible by 2 → Answer: C
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3) 7717
- Odd → not divisible by 2, 5, 6, 10
- Sum: 7+7+1+7 = 22 → not divisible by 3 or 9
→ None → Answer: C
Wait — option D says “3,9” but sum is 22 → no. Option B has too many. So yes, C) None
But wait — let me double-check: 7717 ÷ 3? 3×2572=7716 → remainder 1 → not divisible. Correct.
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4) 7720
- Ends in 0 → divisible by 2, 5, 10
- Sum: 7+7+2+0 = 16 → not divisible by 3 → not by 6 or 9
→ So only 2, 5, 10 → Answer: D
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5) 7723
- Odd → not 2, 5, 6, 10
- Sum: 7+7+2+3 = 19 → not divisible by 3 or 9
→ None → Answer: D
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6) 7727
- Odd → not 2, 5, 6, 10
- Sum: 7+7+2+7 = 23 → not divisible by 3 or 9
→ None → Answer: B
Wait — option B is “None”, yes.
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7) 7730
- Ends in 0 → divisible by 2, 5, 10
- Sum: 7+7+3+0 = 17 → not divisible by 3 → not by 6 or 9
→ So 2, 5, 10 → Answer: B
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8) 7733
- Odd → not 2, 5, 6, 10
- Sum: 7+7+3+3 = 20 → not divisible by 3 or 9
→ None → Answer: C
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9) 7737
- Odd → not 2, 5, 6, 10
- Sum: 7+7+3+7 = 24 → divisible by 3 → check 9? 24÷9=2.66… → no
→ Divisible by 3 only → Answer: D
Wait — option D is “3”, yes.
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10) 7740
- Ends in 0 → divisible by 2, 5, 10
- Sum: 7+7+4+0 = 18 → divisible by 3 and 9 → so also by 6
→ So divisible by: 2, 3, 5, 6, 9, 10 → Answer: D
---
11) 7743
- Odd → not 2, 5, 6, 10
- Sum: 7+7+4+3 = 21 → divisible by 3 → not by 9 (21÷9=2.33…)
→ Divisible by 3 only → Answer: A
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12) 7746
- Even → divisible by 2
- Sum: 7+7+4+6 = 24 → divisible by 3 → so also by 6
- Not ending in 0 or 5 → not by 5 or 10
- 24 not divisible by 9 → not by 9
→ So divisible by 2, 3, 6 → Answer: C
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13) 7750
- Ends in 0 → divisible by 2, 5, 10
- Sum: 7+7+5+0 = 19 → not divisible by 3 → not by 6 or 9
→ So 2, 5, 10 → Answer: D
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14) 7756
- Even → divisible by 2
- Sum: 7+7+5+6 = 25 → not divisible by 3 → not by 6 or 9
- Not ending in 0 or 5 → not by 5 or 10
→ Only divisible by 2 → Answer: C
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15) 7753
- Odd → not 2, 5, 6, 10
- Sum: 7+7+5+3 = 22 → not divisible by 3 or 9
→ None → Answer: B
(Note: Option B says “None”, though it's written as “BNone” — probably typo)
---
16) 7763
- Odd → not 2, 5, 6, 10
- Sum: 7+7+6+3 = 23 → not divisible by 3 or 9
→ None → Answer: A
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17) 7759
- Odd → not 2, 5, 6, 10
- Sum: 7+7+5+9 = 28 → not divisible by 3 or 9
→ None → Answer: A
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18) 7769
- Odd → not 2, 5, 6, 10
- Sum: 7+7+6+9 = 29 → not divisible by 3 or 9
→ None → Answer: A
Wait — option A is “None”, yes.
But let me check: 7769 ÷ 3? 3×2589=7767 → remainder 2 → correct.
---
Now compiling all answers:
1) A
2) C
3) C
4) D
5) D
6) B
7) B
8) C
9) D
10) D
11) A
12) C
13) D
14) C
15) B
16) A
17) A
18) A
Final Answer:
1-A, 2-C, 3-C, 4-D, 5-D, 6-B, 7-B, 8-C, 9-D, 10-D, 11-A, 12-C, 13-D, 14-C, 15-B, 16-A, 17-A, 18-A
We’ll use basic divisibility rules:
- Divisible by 2: Last digit is even (0, 2, 4, 6, 8)
- Divisible by 3: Sum of digits is divisible by 3
- Divisible by 5: Ends in 0 or 5
- Divisible by 6: Must be divisible by both 2 and 3
- Divisible by 9: Sum of digits is divisible by 9
- Divisible by 10: Ends in 0
---
1) 7710
- Ends in 0 → divisible by 2, 5, 10
- Sum of digits: 7+7+1+0 = 15 → divisible by 3 → so also divisible by 6
→ So divisible by: 2, 3, 5, 6, 10 → Answer: A
---
2) 7714
- Ends in 4 → divisible by 2
- Sum: 7+7+1+4 = 19 → not divisible by 3 → not by 6 or 9
- Doesn’t end in 0 or 5 → not by 5 or 10
→ Only divisible by 2 → Answer: C
---
3) 7717
- Odd → not divisible by 2, 5, 6, 10
- Sum: 7+7+1+7 = 22 → not divisible by 3 or 9
→ None → Answer: C
Wait — option D says “3,9” but sum is 22 → no. Option B has too many. So yes, C) None
But wait — let me double-check: 7717 ÷ 3? 3×2572=7716 → remainder 1 → not divisible. Correct.
---
4) 7720
- Ends in 0 → divisible by 2, 5, 10
- Sum: 7+7+2+0 = 16 → not divisible by 3 → not by 6 or 9
→ So only 2, 5, 10 → Answer: D
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5) 7723
- Odd → not 2, 5, 6, 10
- Sum: 7+7+2+3 = 19 → not divisible by 3 or 9
→ None → Answer: D
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6) 7727
- Odd → not 2, 5, 6, 10
- Sum: 7+7+2+7 = 23 → not divisible by 3 or 9
→ None → Answer: B
Wait — option B is “None”, yes.
---
7) 7730
- Ends in 0 → divisible by 2, 5, 10
- Sum: 7+7+3+0 = 17 → not divisible by 3 → not by 6 or 9
→ So 2, 5, 10 → Answer: B
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8) 7733
- Odd → not 2, 5, 6, 10
- Sum: 7+7+3+3 = 20 → not divisible by 3 or 9
→ None → Answer: C
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9) 7737
- Odd → not 2, 5, 6, 10
- Sum: 7+7+3+7 = 24 → divisible by 3 → check 9? 24÷9=2.66… → no
→ Divisible by 3 only → Answer: D
Wait — option D is “3”, yes.
---
10) 7740
- Ends in 0 → divisible by 2, 5, 10
- Sum: 7+7+4+0 = 18 → divisible by 3 and 9 → so also by 6
→ So divisible by: 2, 3, 5, 6, 9, 10 → Answer: D
---
11) 7743
- Odd → not 2, 5, 6, 10
- Sum: 7+7+4+3 = 21 → divisible by 3 → not by 9 (21÷9=2.33…)
→ Divisible by 3 only → Answer: A
---
12) 7746
- Even → divisible by 2
- Sum: 7+7+4+6 = 24 → divisible by 3 → so also by 6
- Not ending in 0 or 5 → not by 5 or 10
- 24 not divisible by 9 → not by 9
→ So divisible by 2, 3, 6 → Answer: C
---
13) 7750
- Ends in 0 → divisible by 2, 5, 10
- Sum: 7+7+5+0 = 19 → not divisible by 3 → not by 6 or 9
→ So 2, 5, 10 → Answer: D
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14) 7756
- Even → divisible by 2
- Sum: 7+7+5+6 = 25 → not divisible by 3 → not by 6 or 9
- Not ending in 0 or 5 → not by 5 or 10
→ Only divisible by 2 → Answer: C
---
15) 7753
- Odd → not 2, 5, 6, 10
- Sum: 7+7+5+3 = 22 → not divisible by 3 or 9
→ None → Answer: B
(Note: Option B says “None”, though it's written as “BNone” — probably typo)
---
16) 7763
- Odd → not 2, 5, 6, 10
- Sum: 7+7+6+3 = 23 → not divisible by 3 or 9
→ None → Answer: A
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17) 7759
- Odd → not 2, 5, 6, 10
- Sum: 7+7+5+9 = 28 → not divisible by 3 or 9
→ None → Answer: A
---
18) 7769
- Odd → not 2, 5, 6, 10
- Sum: 7+7+6+9 = 29 → not divisible by 3 or 9
→ None → Answer: A
Wait — option A is “None”, yes.
But let me check: 7769 ÷ 3? 3×2589=7767 → remainder 2 → correct.
---
Now compiling all answers:
1) A
2) C
3) C
4) D
5) D
6) B
7) B
8) C
9) D
10) D
11) A
12) C
13) D
14) C
15) B
16) A
17) A
18) A
Final Answer:
1-A, 2-C, 3-C, 4-D, 5-D, 6-B, 7-B, 8-C, 9-D, 10-D, 11-A, 12-C, 13-D, 14-C, 15-B, 16-A, 17-A, 18-A
Parent Tip: Review the logic above to help your child master the concept of divisibility worksheet for 6th graders.
