Prime and Composite Numbers Worksheets (REVISION) PDF | PDF - Free Printable

Let's solve this step by step.

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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 has more than two positive divisors (i.e., it can be divided evenly by numbers other than 1 and itself).
- Note: 1 is neither prime nor composite.

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## Part A) Write if each number is prime or composite.

We'll analyze each number:

1) 15
- Divisible by 1, 3, 5, 15 → more than two factors → Composite

2) 89
- Check divisibility: Not divisible by 2, 3, 5, 7 (next prime is 11, but 11×8=88, 11×9=99 > 89).
- No divisors other than 1 and 89 → Prime

3) 37
- Check primes up to √37 ≈ 6.08 → check 2, 3, 5
- Not divisible by any → Prime

4) 70
- Even number → divisible by 2 → Composite

5) 93
- Sum of digits: 9+3=12 → divisible by 3 → 93 ÷ 3 = 31 → Composite

6) 19
- Check primes up to √19 ≈ 4.3 → check 2, 3
- Not divisible by either → Prime

7) 2
- Only even prime number → Prime

8) 21
- 21 = 3 × 7 → divisible by 3 and 7 → Composite

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✔ Part A Answers:

1) 15 → Composite
2) 89 → Prime
3) 37 → Prime
4) 70 → Composite
5) 93 → Composite
6) 19 → Prime
7) 2 → Prime
8) 21 → Composite

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## Part B) Circle all the prime numbers.

List:
13, 86, 5, 20, 71, 90, 95, 41, 29, 53, 8, 67

Now evaluate each:

- 13 → Prime (only divisible by 1 and 13) → ✔
- 86 → Even → divisible by 2 → Composite
- 5 → Prime → ✔
- 20 → Even → Composite
- 71 → Check divisibility: not divisible by 2,3,5,7 → Prime → ✔
- 90 → Even → Composite
- 95 → Ends in 5 → divisible by 5 → Composite
- 41 → Check up to √41≈6.4 → not divisible by 2,3,5 → Prime → ✔
- 29 → Not divisible by 2,3,5 → Prime → ✔
- 53 → Check up to √53≈7.3 → not divisible by 2,3,5,7 → Prime → ✔
- 8 → Even → Composite
- 67 → Check up to √67≈8.2 → not divisible by 2,3,5,7 → Prime → ✔

✔ Prime numbers to circle:

13, 5, 71, 41, 29, 53, 67

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## Part C) Circle all the composite numbers.

List:
66, 3, 82, 16, 9, 59, 47, 75, 97, 38, 61, 44

Evaluate each:

- 66 → Even → divisible by 2 → Composite → ✔
- 3 → Prime → ✘
- 82 → Even → Composite → ✔
- 16 → Even → Composite → ✔
- 9 → 3×3 → Composite → ✔
- 59 → Check up to √59≈7.7 → not divisible by 2,3,5,7 → Prime → ✘
- 47 → Prime → ✘
- 75 → Ends in 5 → divisible by 5 → Composite → ✔
- 97 → Prime (check up to √97≈9.8 → not divisible by 2,3,5,7) → ✘
- 38 → Even → Composite → ✔
- 61 → Prime → ✘
- 44 → Even → Composite → ✔

✔ Composite numbers to circle:

66, 82, 16, 9, 75, 38, 44

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✔ Final Answers:

#### A)
1) 15 → Composite
2) 89 → Prime
3) 37 → Prime
4) 70 → Composite
5) 93 → Composite
6) 19 → Prime
7) 2 → Prime
8) 21 → Composite

#### B) Circle: 13, 5, 71, 41, 29, 53, 67

#### C) Circle: 66, 82, 16, 9, 75, 38, 44

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