Prime and Composite Numbers worksheet with a table for identifying factors and classifying numbers.

Let's solve the problem step by step.

We are given a table with numbers, and we need to:

1. List all the factors of each number.
2. Determine whether the number is prime or composite.

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🔹 Definitions:

- A prime number has exactly two distinct positive factors: 1 and itself.
- A composite number has more than two factors.

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Now, let’s go through each number one by one.

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1. 25

- Already filled in:
- Factors: 1, 5, 25
- Prime or Composite: Composite ✔
(Because it has more than two factors: 1, 5, 25)

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2. 36

- Find all factors of 36:
1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36

So, factors: 1, 2, 3, 4, 6, 9, 12, 18, 36

- More than two factors → Composite

✔ Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36
✔ Prime or Composite: Composite

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3. 43

- Check if 43 is divisible by any number from 2 to √43 ≈ 6.5
Try: 2 → no (odd)
3 → 4+3=7, not divisible by 3
5 → doesn’t end in 0 or 5
7 → 7×6=42, 7×7=49 > 43 → not divisible

- Only factors: 1 and 43 → Prime

✔ Factors: 1, 43
✔ Prime or Composite: Prime

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4. 47

- Check divisibility up to √47 ≈ 6.8
Not divisible by 2, 3, 5, or 7
47 ÷ 2 = 23.5 → no
47 ÷ 3 ≈ 15.67 → no
47 ÷ 5 = 9.4 → no
47 ÷ 7 ≈ 6.7 → no

- Only factors: 1 and 47 → Prime

✔ Factors: 1, 47
✔ Prime or Composite: Prime

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5. 51

- Check divisibility:
51 ÷ 3 = 17 → yes! Because 5+1=6 → divisible by 3
So, 3 × 17 = 51

- Factors: 1, 3, 17, 51 → more than two → Composite

✔ Factors: 1, 3, 17, 51
✔ Prime or Composite: Composite

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6. 55

- Ends in 5 → divisible by 5
55 ÷ 5 = 11
So: 5 × 11 = 55

- Factors: 1, 5, 11, 55 → Composite

✔ Factors: 1, 5, 11, 55
✔ Prime or Composite: Composite

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7. 59

- Check divisibility up to √59 ≈ 7.7
Not divisible by 2, 3, 5, 7
59 ÷ 2 = 29.5 → no
59 ÷ 3 ≈ 19.67 → no
59 ÷ 5 = 11.8 → no
59 ÷ 7 ≈ 8.4 → no

- Only factors: 1 and 59 → Prime

✔ Factors: 1, 59
✔ Prime or Composite: Prime

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8. 60

- Many factors:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10

- Factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 → many → Composite

✔ Factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
✔ Prime or Composite: Composite

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9. 61

- Check divisibility up to √61 ≈ 7.8
Not divisible by 2, 3, 5, 7
61 ÷ 2 = 30.5 → no
61 ÷ 3 ≈ 20.33 → no
61 ÷ 5 = 12.2 → no
61 ÷ 7 ≈ 8.7 → no

- Only factors: 1 and 61 → Prime

✔ Factors: 1, 61
✔ Prime or Composite: Prime

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✔ Final Completed Table:

| Number | Factors | Prime or Composite |
|--------|----------------------------------------------|--------------------|
| 25 | 1, 5, 25 | Composite |
| 36 | 1, 2, 3, 4, 6, 9, 12, 18, 36 | Composite |
| 43 | 1, 43 | Prime |
| 47 | 1, 47 | Prime |
| 51 | 1, 3, 17, 51 | Composite |
| 55 | 1, 5, 11, 55 | Composite |
| 59 | 1, 59 | Prime |
| 60 | 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 | Composite |
| 61 | 1, 61 | Prime |

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📝 Summary:

- Prime numbers: 43, 47, 59, 61
- Composite numbers: 25, 36, 51, 55, 60

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