Let's solve the factoring worksheet step by step. The task is to
list all the factors for each number between 4 and 100.
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🔹 What are factors?
Factors of a number are the whole numbers that divide it evenly (with no remainder). For example, the factors of 18 are:
1, 2, 3, 6, 9, 18 — because these numbers divide 18 exactly.
We'll find all such factors for each number listed.
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Now let’s go through each number:
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1. 86
Find all numbers that divide 86:
- 1 × 86 = 86
- 2 × 43 = 86
- No other numbers work (check up to √86 ≈ 9.2)
So, factors:
1, 2, 43, 86
✔ Answer: 1, 2, 43, 86
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2. 7
7 is a prime number.
Only divisible by 1 and itself.
So, factors:
1, 7
✔ Answer: 1, 7
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3. 12
Divisors:
- 1 × 12 = 12
- 2 × 6 = 12
- 3 × 4 = 12
So, factors:
1, 2, 3, 4, 6, 12
✔ Answer: 1, 2, 3, 4, 6, 12
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4. 77
Check divisors:
- 1 × 77 = 77
- 7 × 11 = 77
No others.
So, factors:
1, 7, 11, 77
✔ Answer: 1, 7, 11, 77
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5. 38
- 1 × 38 = 38
- 2 × 19 = 38
So, factors:
1, 2, 19, 38
✔ Answer: 1, 2, 19, 38
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6. 52
- 1 × 52 = 52
- 2 × 26 = 52
- 4 × 13 = 52
So, factors:
1, 2, 4, 13, 26, 52
✔ Answer: 1, 2, 4, 13, 26, 52
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7. 9
- 1 × 9 = 9
- 3 × 3 = 9
So, factors:
1, 3, 9
✔ Answer: 1, 3, 9
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8. 73
73 is a prime number (only divisible by 1 and 73).
So, factors:
1, 73
✔ Answer: 1, 73
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9. 98
- 1 × 98 = 98
- 2 × 49 = 98
- 7 × 14 = 98
- Also, 49 = 7×7 → so 7 appears twice
So, factors:
1, 2, 7, 14, 49, 98
✔ Answer: 1, 2, 7, 14, 49, 98
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10. 24
- 1 × 24 = 24
- 2 × 12 = 24
- 3 × 8 = 24
- 4 × 6 = 24
So, factors:
1, 2, 3, 4, 6, 8, 12, 24
✔ Answer: 1, 2, 3, 4, 6, 8, 12, 24
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11. 6
- 1 × 6 = 6
- 2 × 3 = 6
So, factors:
1, 2, 3, 6
✔ Answer: 1, 2, 3, 6
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12. 80
- 1 × 80 = 80
- 2 × 40 = 80
- 4 × 20 = 80
- 5 × 16 = 80
- 8 × 10 = 80
So, factors:
1, 2, 4, 5, 8, 10, 16, 20, 40, 80
✔ Answer: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
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✔ Final Answers:
| Number | Factors |
|--------|---------|
| 1. 86 | 1, 2, 43, 86 |
| 2. 7 | 1, 7 |
| 3. 12 | 1, 2, 3, 4, 6, 12 |
| 4. 77 | 1, 7, 11, 77 |
| 5. 38 | 1, 2, 19, 38 |
| 6. 52 | 1, 2, 4, 13, 26, 52 |
| 7. 9 | 1, 3, 9 |
| 8. 73 | 1, 73 |
| 9. 98 | 1, 2, 7, 14, 49, 98 |
| 10. 24 | 1, 2, 3, 4, 6, 8, 12, 24 |
| 11. 6 | 1, 2, 3, 6 |
| 12. 80 | 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 |
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📝 Tips for Finding Factors:
1. Start with 1 and the number itself.
2. Try dividing by small numbers (2, 3, 4, etc.) until you reach the square root.
3. If a number divides evenly, both the divisor and quotient are factors.
4. List them in order from smallest to largest.
This method helps avoid missing any factors.
Let me know if you'd like this as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of factors worksheet 4th grade.
