Prime and Composite Numbers Worksheet - Identify factors and classify 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.

---

🔹 Definitions:

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

---

Now let’s go through each number:

---

#### 1. Number: 25
- Already given: Factors = 1, 5, 25
- Has more than two factors → Composite

✔ Done.

---

#### 2. Number: 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

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

---

#### 3. Number: 43
- Check if it has any divisors other than 1 and itself.
- Try dividing by primes less than √43 ≈ 6.5: 2, 3, 5
- 43 ÷ 2 = 21.5 → not divisible
- 43 ÷ 3 ≈ 14.33 → not divisible
- 43 ÷ 5 = 8.6 → not divisible
- No divisors → only factors are 1 and 43
- So → Prime

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

---

#### 4. Number: 47
- √47 ≈ 6.8, so check divisibility by 2, 3, 5
- 47 ÷ 2 = 23.5 → no
- 47 ÷ 3 ≈ 15.67 → no
- 47 ÷ 5 = 9.4 → no
- Only factors: 1 and 47
→ Prime

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

---

#### 5. Number: 51
- Check divisibility:
- 51 ÷ 3 = 17 → yes! (since 5+1=6, divisible by 3)
- So factors: 1, 3, 17, 51
- More than two factors → Composite

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

---

#### 6. Number: 55
- Divisible by 5? Ends in 5 → yes
- 55 ÷ 5 = 11
- So factors: 1, 5, 11, 55
- More than two → Composite

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

---

#### 7. Number: 59
- √59 ≈ 7.7 → check 2, 3, 5, 7
- 59 ÷ 2 = 29.5 → no
- 59 ÷ 3 ≈ 19.67 → no
- 59 ÷ 5 = 11.8 → no
- 59 ÷ 7 ≈ 8.43 → no
- Only factors: 1 and 59 → Prime

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

---

#### 8. Number: 60
- Many factors:
- 1 × 60
- 2 × 30
- 3 × 20
- 4 × 15
- 5 × 12
- 6 × 10
- So factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Clearly composite

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

---

#### 9. Number: 61
- √61 ≈ 7.8 → check 2, 3, 5, 7
- 61 ÷ 2 = 30.5 → no
- 61 ÷ 3 ≈ 20.33 → no
- 61 ÷ 5 = 12.2 → no
- 61 ÷ 7 ≈ 8.71 → no
- Only factors: 1 and 61 → Prime

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

---

✔ 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 |

---

📝 Summary:

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

Let me know if you'd like this as a printable version or need help understanding any part!