Prime and Composite Numbers worksheet for identifying prime and composite numbers.

Sure! Let’s solve this worksheet by identifying each number as prime or composite.

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🔢 Definitions:

- Prime Number: A number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
- Composite Number: A number greater than 1 that has more than two distinct positive divisors (i.e., it can be divided evenly by numbers other than 1 and itself).

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Now let’s go through each number one by one:

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✔ 1) 67

Check divisibility: Not divisible by 2, 3, 5, 7, 11... up to √67 (~8.1).
→ Prime

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✔ 2) 530

Ends in 0 → divisible by 2 and 5 → 530 = 2 × 5 × 53
→ Composite

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✔ 3) 825

Ends in 5 → divisible by 5 → 825 ÷ 5 = 165 → also divisible by 3 (8+2+5=15)
→ Composite

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✔ 4) 19

Not divisible by 2, 3, 5, 7, 11, 13, 17 → only factors are 1 and 19
→ Prime

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✔ 5) 41

Check primes up to √41 (~6.4): not divisible by 2, 3, 5 → only factors 1 and 41
→ Prime

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✔ 6) 87

Sum of digits: 8 + 7 = 15 → divisible by 3 → 87 ÷ 3 = 29
→ Composite

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✔ 7) 62

Even number → divisible by 2 → 62 = 2 × 31
→ Composite

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✔ 8) 293

Check divisibility:
√293 ≈ 17.1 → check primes up to 17: 2, 3, 5, 7, 11, 13, 17
- Not even → not divisible by 2
- Sum digits: 2+9+3=14 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- 293 ÷ 7 ≈ 41.85 → not divisible
- 293 ÷ 11 ≈ 26.6 → no
- 293 ÷ 13 ≈ 22.5 → no
- 293 ÷ 17 ≈ 17.2 → no
→ Prime

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✔ 9) 157

√157 ≈ 12.5 → check primes up to 11: 2, 3, 5, 7, 11
- Odd → not divisible by 2
- 1+5+7=13 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- 157 ÷ 7 ≈ 22.4 → no
- 157 ÷ 11 ≈ 14.27 → no
→ Prime

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✔ 10) 69

Sum digits: 6+9=15 → divisible by 3 → 69 ÷ 3 = 23
→ Composite

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✔ 11) 91

Check: 91 = 7 × 13 → divisible by 7 and 13
→ Composite

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✔ 12) 37

Check primes up to √37 (~6.08): 2, 3, 5 → none divide 37
→ Prime

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✔ 13) 383

√383 ≈ 19.5 → check primes up to 19: 2, 3, 5, 7, 11, 13, 17, 19
- Odd → not divisible by 2
- 3+8+3=14 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- 383 ÷ 7 ≈ 54.7 → no
- 383 ÷ 11 ≈ 34.8 → no
- 383 ÷ 13 ≈ 29.46 → no
- 383 ÷ 17 ≈ 22.5 → no
- 383 ÷ 19 ≈ 20.15 → no
→ Prime

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✔ 14) 445

Ends in 5 → divisible by 5 → 445 ÷ 5 = 89
→ Composite

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✔ 15) 16

Even → divisible by 2 → 16 = 2⁴ → many factors
→ Composite

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✔ 16) 31

Check primes up to √31 (~5.5): 2, 3, 5 → none divide 31
→ Prime

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✔ 17) 79

Check primes up to √79 (~8.9): 2, 3, 5, 7
- Odd → not divisible by 2
- 7+9=16 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- 79 ÷ 7 ≈ 11.28 → no
→ Prime

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✔ 18) 926

Even → divisible by 2 → 926 = 2 × 463
→ Composite

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## 📝 Final Answers:

1) Prime
2) Composite
3) Composite
4) Prime
5) Prime
6) Composite
7) Composite
8) Prime
9) Prime
10) Composite
11) Composite
12) Prime
13) Prime
14) Composite
15) Composite
16) Prime
17) Prime
18) Composite

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✔ You’re all set! This worksheet helps reinforce understanding of prime vs. composite numbers — great practice for number theory basics!