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

Let's solve the problem step by step.

We are asked to determine whether each number is prime or composite.

Definitions:

- A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
- A composite number is a natural number greater than 1 that is not prime (i.e., it has factors other than 1 and itself).

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Now, let’s analyze each number:

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1) 67
Check divisibility:
- Not even → not divisible by 2
- Sum of digits: 6 + 7 = 13 → not divisible by 3
- Doesn't end in 0 or 5 → not divisible by 5
- Check divisibility by primes up to √67 ≈ 8.2: try 7 → 67 ÷ 7 ≈ 9.57 → not divisible
→ No divisors other than 1 and 67 → Prime

✔ Prime

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2) 530
Ends in 0 → divisible by 10 → divisible by 2 and 5 → Composite

✔ Composite

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3) 825
Ends in 5 → divisible by 5 → Composite

✔ Composite

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4) 19
Check divisibility:
- Not divisible by 2, 3, 5, 7 (since 7×2=14, 7×3=21 >19)
→ Only divisible by 1 and 19 → Prime

✔ Prime

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5) 41
Check primes up to √41 ≈ 6.4 → check 2, 3, 5
- Odd → not divisible by 2
- 4+1=5 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
→ Prime

✔ Prime

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6) 87
Sum of digits: 8 + 7 = 15 → divisible by 3 → 87 ÷ 3 = 29 → Composite

✔ Composite

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7) 62
Even number → divisible by 2 → Composite

✔ Composite

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8) 293
Check divisibility:
- Not even
- Sum: 2+9+3=14 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- Try 7: 7×41=287, 293 - 287 = 6 → not divisible
- Try 11: 11×26 = 286, 293 - 286 = 7 → not divisible
- Try 13: 13×22 = 286, 293 - 286 = 7 → no
- Try 17: 17×17 = 289, 293 - 289 = 4 → no
- Next prime is 19 → 19×15 = 285, 293 - 285 = 8 → no
√293 ≈ 17.1 → we've checked all primes ≤ 17 → no divisors → Prime

✔ Prime

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9) 157
Check divisibility:
- Odd → not divisible by 2
- Sum: 1+5+7=13 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- Try 7: 7×22 = 154, 157 - 154 = 3 → not divisible
- Try 11: 11×14 = 154, 157 - 154 = 3 → no
- Try 13: 13×12 = 156, 157 - 156 = 1 → no
√157 ≈ 12.5 → only need to check up to 13 → no divisors → Prime

✔ Prime

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10) 69
Sum: 6+9=15 → divisible by 3 → 69 ÷ 3 = 23 → Composite

✔ Composite

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11) 91
Check: 7×13 = 91 → divisible by 7 and 13 → Composite

✔ Composite

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12) 37
Check:
- Not divisible by 2, 3, 5
- Try 7: 7×5 = 35, 37 - 35 = 2 → not divisible
√37 ≈ 6.1 → check primes up to 5 → no divisors → Prime

✔ Prime

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13) 383
Check divisibility:
- Odd
- Sum: 3+8+3=14 → not divisible by 3
- Not ending in 0 or 5 → not divisible by 5
- Try 7: 7×54 = 378, 383 - 378 = 5 → no
- Try 11: 11×34 = 374, 383 - 374 = 9 → no
- Try 13: 13×29 = 377, 383 - 377 = 6 → no
- Try 17: 17×22 = 374, 383 - 374 = 9 → no
- Try 19: 19×20 = 380, 383 - 380 = 3 → no
- Try 23: 23×16 = 368, 383 - 368 = 15 → no
- Try 29: 29×13 = 377, 383 - 377 = 6 → no
- Try 31: 31×12 = 372, 383 - 372 = 11 → no
√383 ≈ 19.5 → we’ve checked up to 19 → no divisors → Prime

✔ Prime

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14) 445
Ends in 5 → divisible by 5 → Composite

✔ Composite

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15) 16
Even number → divisible by 2 → Composite

✔ Composite

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16) 31
Check:
- Odd, sum 3+1=4 → not divisible by 3
- Not divisible by 5
- Try 7: 7×4 = 28, 31 - 28 = 3 → no
√31 ≈ 5.6 → check up to 5 → no divisors → Prime

✔ Prime

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17) 79
- Odd, sum 7+9=16 → not divisible by 3
- Not divisible by 5
- Try 7: 7×11 = 77, 79 - 77 = 2 → no
- Try 11: 11×7 = 77 → same
√79 ≈ 8.9 → check up to 7 → no divisors → Prime

✔ Prime

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18) 926
Even number → divisible by 2 → Composite

✔ Composite

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Final Answers:

1) 67 → Prime
2) 530 → Composite
3) 825 → Composite
4) 19 → Prime
5) 41 → Prime
6) 87 → Composite
7) 62 → Composite
8) 293 → Prime
9) 157 → Prime
10) 69 → Composite
11) 91 → Composite
12) 37 → Prime
13) 383 → Prime
14) 445 → Composite
15) 16 → Composite
16) 31 → Prime
17) 79 → Prime
18) 926 → Composite

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✔ Answer Key:
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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