Prime and Composite Numbers worksheet for students to complete.

Let’s go step by step to fill in the table for each number. We need to find all the factors of each number, then decide if it’s prime or composite.

Remember:
- A prime number has exactly two factors: 1 and itself.
- A composite number has more than two factors.
- The number 1 is neither prime nor composite — but none of our numbers are 1, so we’re safe!

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Number: 36

Find all factors:
Start from 1 and go up:
1 × 36 = 36 → factors: 1, 36
2 × 18 = 36 → factors: 2, 18
3 × 12 = 36 → factors: 3, 12
4 × 9 = 36 → factors: 4, 9
6 × 6 = 36 → factor: 6 (only count once)

So factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 → more than 2 → Composite

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Number: 43

Check if any number divides 43 besides 1 and 43.
Try dividing by 2? No — it’s odd.
By 3? 4+3=7 → not divisible by 3.
By 5? Doesn’t end in 0 or 5.
By 7? 7×6=42, 7×7=49 → too big.
No other divisors → only factors: 1, 43 → Prime

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Number: 47

Same idea. Try small primes:
Not even → not divisible by 2.
4+7=11 → not divisible by 3.
Doesn’t end in 0 or 5 → not divisible by 5.
7×6=42, 7×7=49 → too big.
Next prime is 11 → 11×4=44, 11×5=55 → too big.
So only factors: 1, 47 → Prime

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Number: 51

Check divisibility:
Odd → not divisible by 2.
5+1=6 → divisible by 3!
51 ÷ 3 = 17 → so factors include 3 and 17.
Also 1 and 51.
Factors: 1, 3, 17, 51 → more than 2 → Composite

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Number: 55

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

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Number: 59

Check small primes:
Odd → not divisible by 2.
5+9=14 → not divisible by 3.
Doesn’t end in 0 or 5 → not divisible by 5.
7×8=56, 7×9=63 → too big.
11×5=55, 11×6=66 → too big.
So only factors: 1, 59 → Prime

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Number: 60

This one has lots of factors. Let’s list them:
1 × 60
2 × 30
3 × 20
4 × 15
5 × 12
6 × 10
Also 60 ÷ 6 = 10 → already have that.
So factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 → definitely Composite

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Number: 61

Check small primes:
Odd → not divisible by 2.
6+1=7 → not divisible by 3.
Doesn’t end in 0 or 5 → not divisible by 5.
7×8=56, 7×9=63 → too big.
11×5=55, 11×6=66 → too big.
So only factors: 1, 61 → Prime

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Now let’s put it all together in the table format:

| 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:
The completed table is as shown above with correct factors and classification for each number.