301 Moved Permanently - Free Printable
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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 solve each question on Worksheet-2 using the divisibility rules for the numbers 2, 3, 5, 6, 9, and 10.
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- 2: Number ends in an even digit (0, 2, 4, 6, 8).
- 3: Sum of digits is divisible by 3.
- 5: Ends in 0 or 5.
- 6: Divisible by both 2 and 3.
- 9: Sum of digits is divisible by 9.
- 10: Ends in 0.
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Now let’s go through each problem one by one:
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- Ends in 0 → divisible by 2, 5, 10
- Sum of digits: 1 + 0 + 0 = 1 → not divisible by 3 → not divisible by 3, 6, 9
- So divisible by: 2, 5, 10
✔ Answer: A) 2, 5, 10
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- Ends in 5 → divisible by 5
- Sum: 7 + 5 = 12 → divisible by 3 → so divisible by 3
- Not even → not divisible by 2 → so not divisible by 6 or 10
- 12 not divisible by 9 → not divisible by 9
- So divisible by: 3, 5
✔ Answer: A) 3, 5
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- Even → divisible by 2
- Sum: 6 + 8 = 14 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: D) 2
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- Odd → not divisible by 2, 6, 10
- Sum: 8 + 3 = 11 → not divisible by 3 → not divisible by 3, 9
- Doesn’t end in 0 or 5 → not divisible by 5
- So none of the listed divisors work
✔ Answer: D) None
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- Even → divisible by 2
- Sum: 5 + 2 = 7 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn't end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: C) 2
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- Ends in 5 → divisible by 5
- Sum: 6 + 5 = 11 → not divisible by 3 → not divisible by 3, 9
- Odd → not divisible by 2 → not divisible by 6, 10
- So only divisible by 5
✔ Answer: C) 5
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- Even → divisible by 2
- Sum: 3 + 6 + 8 = 17 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: B) 2
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- Even → divisible by 2
- Sum: 3 + 7 + 4 = 14 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: B) 2
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- Ends in 5 → divisible by 5
- Sum: 3 + 5 + 5 = 13 → not divisible by 3 → not divisible by 3, 6, 9
- Odd → not divisible by 2 → not divisible by 6, 10
- So only divisible by 5
✔ Answer: C) 5
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- Even → divisible by 2
- Sum: 3 + 8 + 4 = 15 → divisible by 3 → divisible by 3
- So divisible by 6 (since divisible by 2 and 3)
- But not divisible by 9 (15 not divisible by 9)
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So divisible by: 2, 3, 6
✔ Answer: C) 2, 3, 6
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- Odd → not divisible by 2, 6, 10
- Sum: 3 + 7 + 1 = 11 → not divisible by 3 → not divisible by 3, 9
- Doesn’t end in 0 or 5 → not divisible by 5
- So none of the options work
✔ Answer: D) None
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- Odd → not divisible by 2, 6, 10
- Sum: 4 + 0 + 1 = 5 → not divisible by 3 → not divisible by 3, 9
- Doesn’t end in 0 or 5 → not divisible by 5
- So none apply
✔ Answer: D) None
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- Even → divisible by 2
- Sum: 3 + 8 + 8 = 19 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: A) 2
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- Even → divisible by 2
- Sum: 3 + 9 + 4 = 16 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: D) 2
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- Odd → not divisible by 2, 6, 10
- Sum: 3 + 8 + 1 = 12 → divisible by 3 → divisible by 3
- 12 not divisible by 9 → not divisible by 9
- Doesn’t end in 0 or 5 → not divisible by 5
- So divisible by 3
✔ Answer: A) 3
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- Even → divisible by 2
- Sum: 3 + 7 + 8 = 18 → divisible by 3 and 9 → divisible by 3, 9
- So divisible by 6 (since divisible by 2 and 3)
- Ends in 8 → not divisible by 5 or 10
- So divisible by: 2, 3, 6, 9
✔ Answer: A) 2, 3, 6, 9
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| Q | Answer |
|---|--------|
| 85 | A) 2, 5, 10 |
| 86 | A) 3, 5 |
| 87 | D) 2 |
| 88 | D) None |
| 89 | C) 2 |
| 90 | C) 5 |
| 91 | B) 2 |
| 92 | B) 2 |
| 93 | C) 5 |
| 94 | C) 2, 3, 6 |
| 95 | D) None |
| 96 | D) None |
| 97 | A) 2 |
| 98 | D) 2 |
| 99 | A) 3 |
| 100| A) 2, 3, 6, 9 |
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🔢 Divisibility Rules Recap:
- 2: Number ends in an even digit (0, 2, 4, 6, 8).
- 3: Sum of digits is divisible by 3.
- 5: Ends in 0 or 5.
- 6: Divisible by both 2 and 3.
- 9: Sum of digits is divisible by 9.
- 10: Ends in 0.
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Now let’s go through each problem one by one:
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85) 100
- Ends in 0 → divisible by 2, 5, 10
- Sum of digits: 1 + 0 + 0 = 1 → not divisible by 3 → not divisible by 3, 6, 9
- So divisible by: 2, 5, 10
✔ Answer: A) 2, 5, 10
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86) 75
- Ends in 5 → divisible by 5
- Sum: 7 + 5 = 12 → divisible by 3 → so divisible by 3
- Not even → not divisible by 2 → so not divisible by 6 or 10
- 12 not divisible by 9 → not divisible by 9
- So divisible by: 3, 5
✔ Answer: A) 3, 5
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87) 68
- Even → divisible by 2
- Sum: 6 + 8 = 14 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: D) 2
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88) 83
- Odd → not divisible by 2, 6, 10
- Sum: 8 + 3 = 11 → not divisible by 3 → not divisible by 3, 9
- Doesn’t end in 0 or 5 → not divisible by 5
- So none of the listed divisors work
✔ Answer: D) None
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89) 52
- Even → divisible by 2
- Sum: 5 + 2 = 7 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn't end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: C) 2
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90) 65
- Ends in 5 → divisible by 5
- Sum: 6 + 5 = 11 → not divisible by 3 → not divisible by 3, 9
- Odd → not divisible by 2 → not divisible by 6, 10
- So only divisible by 5
✔ Answer: C) 5
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91) 368
- Even → divisible by 2
- Sum: 3 + 6 + 8 = 17 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: B) 2
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92) 374
- Even → divisible by 2
- Sum: 3 + 7 + 4 = 14 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: B) 2
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93) 355
- Ends in 5 → divisible by 5
- Sum: 3 + 5 + 5 = 13 → not divisible by 3 → not divisible by 3, 6, 9
- Odd → not divisible by 2 → not divisible by 6, 10
- So only divisible by 5
✔ Answer: C) 5
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94) 384
- Even → divisible by 2
- Sum: 3 + 8 + 4 = 15 → divisible by 3 → divisible by 3
- So divisible by 6 (since divisible by 2 and 3)
- But not divisible by 9 (15 not divisible by 9)
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So divisible by: 2, 3, 6
✔ Answer: C) 2, 3, 6
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95) 371
- Odd → not divisible by 2, 6, 10
- Sum: 3 + 7 + 1 = 11 → not divisible by 3 → not divisible by 3, 9
- Doesn’t end in 0 or 5 → not divisible by 5
- So none of the options work
✔ Answer: D) None
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96) 401
- Odd → not divisible by 2, 6, 10
- Sum: 4 + 0 + 1 = 5 → not divisible by 3 → not divisible by 3, 9
- Doesn’t end in 0 or 5 → not divisible by 5
- So none apply
✔ Answer: D) None
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97) 388
- Even → divisible by 2
- Sum: 3 + 8 + 8 = 19 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: A) 2
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98) 394
- Even → divisible by 2
- Sum: 3 + 9 + 4 = 16 → not divisible by 3 → not divisible by 3, 6, 9
- Doesn’t end in 0 or 5 → not divisible by 5 or 10
- So only divisible by 2
✔ Answer: D) 2
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99) 381
- Odd → not divisible by 2, 6, 10
- Sum: 3 + 8 + 1 = 12 → divisible by 3 → divisible by 3
- 12 not divisible by 9 → not divisible by 9
- Doesn’t end in 0 or 5 → not divisible by 5
- So divisible by 3
✔ Answer: A) 3
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100) 378
- Even → divisible by 2
- Sum: 3 + 7 + 8 = 18 → divisible by 3 and 9 → divisible by 3, 9
- So divisible by 6 (since divisible by 2 and 3)
- Ends in 8 → not divisible by 5 or 10
- So divisible by: 2, 3, 6, 9
✔ Answer: A) 2, 3, 6, 9
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✔ Final Answers:
| Q | Answer |
|---|--------|
| 85 | A) 2, 5, 10 |
| 86 | A) 3, 5 |
| 87 | D) 2 |
| 88 | D) None |
| 89 | C) 2 |
| 90 | C) 5 |
| 91 | B) 2 |
| 92 | B) 2 |
| 93 | C) 5 |
| 94 | C) 2, 3, 6 |
| 95 | D) None |
| 96 | D) None |
| 97 | A) 2 |
| 98 | D) 2 |
| 99 | A) 3 |
| 100| A) 2, 3, 6, 9 |
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Let me know if you'd like this as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of test of divisibility worksheet.
