Prime and Composite Numbers worksheet for grades 4 and 5 | Live ... - Free Printable

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

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

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

4) 19
Check:
- Not divisible by 2, 3, or 5
- √19 ≈ 4.3 → check up to 4
→ Only divisible by 1 and 19 → Prime

5) 41
- Not divisible by 2, 3, 5
- √41 ≈ 6.4 → check up to 5
→ Only divisible by 1 and 41 → Prime

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

7) 62
Even number → divisible by 2 → Composite

8) 293
Check divisibility:
- Odd → not divisible by 2
- Sum: 2+9+3=14 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- Try 7: 293 ÷ 7 ≈ 41.85 → no
- 11: 2 - 9 + 3 = -4 → not divisible by 11
- 13: 13×22 = 286, 293 - 286 = 7 → not divisible
- 17: 17×17 = 289, 293 - 289 = 4 → not divisible
- √293 ≈ 17.1 → so we’re done
→ No divisors → Prime

9) 157
- Odd, not divisible by 3 (1+5+7=13), not by 5
- √157 ≈ 12.5 → check primes up to 11
- 7: 7×22 = 154, 157 - 154 = 3 → not divisible
- 11: 11×14 = 154 → 157 - 154 = 3 → not divisible
→ Prime

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

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

12) 37
- Not divisible by 2, 3, 5
- √37 ≈ 6.1 → check up to 5
→ Only divisible by 1 and 37 → Prime

13) 383
Odd, sum = 3+8+3=14 → not divisible by 3
Not divisible by 5
Try 7: 7×54 = 378, 383 - 378 = 5 → not divisible
11: 3 - 8 + 3 = -2 → not divisible
13: 13×29 = 377, 383 - 377 = 6 → no
17: 17×22 = 374, 383 - 374 = 9 → no
19: 19×20 = 380, 383 - 380 = 3 → no
23: 23×16 = 368, 383 - 368 = 15 → no
√383 ≈ 19.5 → so stop here
→ No divisors → Prime

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

15) 16
Even → divisible by 2 → Composite

16) 31
- Odd, sum = 4 → not divisible by 3
- √31 ≈ 5.6 → check up to 5
→ Only divisible by 1 and 31 → Prime

17) 79
- Odd, sum = 16 → not divisible by 3
- Not divisible by 5
- Try 7: 7×11 = 77, 79 - 77 = 2 → no
- 11: 11×7 = 77 → same
- √79 ≈ 8.9 → check up to 7
→ Only divisible by 1 and 79 → Prime

18) 926
Even → divisible by 2 → 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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