Prime and Composite Numbers Worksheets - 15 Worksheets Library - Free Printable

Explanation:
We need to fill in the table with the factors of each number and then decide whether the number is prime or composite.

Remember:
- A prime number has exactly two positive factors: 1 and itself.
- A composite number has more than two positive factors.
- The number 1 is neither prime nor composite, but it’s not in this list.

Let’s go row by row:

1. 25 — already done: factors are 1, 5, 25 → 3 factors → Composite ✔

2. 36
Find all numbers that divide 36 evenly:
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 → 9 factors → Composite

3. 43
Check divisibility:
- Not even → not divisible by 2
- 4 + 3 = 7 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- Try 7: 7 × 6 = 42, 7 × 7 = 49 → too big
- Try 11: 11 × 3 = 33, 11 × 4 = 44 → too big
No divisors other than 1 and 43 → only 2 factors → Prime

4. 47
Similar check:
- Not even
- 4 + 7 = 11 → not divisible by 3
- Doesn’t end in 0/5
- 7 × 6 = 42, 7 × 7 = 49 → no
- 11 × 4 = 44, 11 × 5 = 55 → no
- √47 ≈ 6.8, so we only need to test primes ≤ 6: 2, 3, 5 — none work
So only factors: 1 and 47 → Prime

5. 51
Check: 5 + 1 = 6 → divisible by 3
51 ÷ 3 = 17
So factors: 1, 3, 17, 51 → 4 factors → Composite

6. 55
Ends in 5 → divisible by 5
55 ÷ 5 = 11
So factors: 1, 5, 11, 55 → 4 factors → Composite

7. 59
Check small primes:
- Not even
- 5 + 9 = 14 → not divisible by 3
- Doesn’t end in 0/5
- 7 × 8 = 56, 7 × 9 = 63 → no
- 11 × 5 = 55, 11 × 6 = 66 → no
√59 ≈ 7.7, so test up to 7: 2, 3, 5, 7 — none divide 59
Only factors: 1 and 59 → Prime

8. 60
Easy: divisible by many numbers
Factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 → many → Composite

9. 61
Check:
- Not even
- 6 + 1 = 7 → not divisible by 3
- Doesn’t end in 0/5
- 7 × 8 = 56, 7 × 9 = 63 → no
- 11 × 5 = 55, 11 × 6 = 66 → no
√61 ≈ 7.8, test primes ≤ 7: 2, 3, 5, 7 — none divide 61
So only 1 and 61 → Prime

Now let’s write the full 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 |

Final Answer:
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