Prime and Composite Numbers Worksheet for Math Education

Let’s solve each part step by step, using the definitions given in the worksheet.

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Definitions from the worksheet:

- Factors are the numbers you multiply to get another number.
- Example: Factors of 6 → 1, 2, 3, 6 (because 1×6=6, 2×3=6)

- Prime numbers have only two factors: 1 and themselves.
- Example: 19 → factors are 1 and 19 → prime

- Composite numbers have more than two factors.
- Example: 10 → factors are 1, 2, 5, 10 → composite

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## a. Number: 4

Step 1: List all factors of 4

We need numbers that multiply to give 4:
- 1 × 4 = 4 → so 1 and 4 are factors
- 2 × 2 = 4 → so 2 is a factor

✔ Factors of 4: 1, 2, 4

Step 2: Is 4 prime or composite?

- How many factors? → 3 factors (1, 2, 4)
- Since it has more than two factors, it is composite

✔ Answer:
- Factors: 1, 2, 4
- 4 is a composite number

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## b. Number: 11

Step 1: List all factors of 11

What numbers multiply to give 11?
- 1 × 11 = 11 → so 1 and 11 are factors
- Try 2: 2×5.5 = 11 → not whole → not a factor
- 3, 4, 5, ... up to 10 — none divide 11 evenly

✔ Factors of 11: 1, 11

Step 2: Is 11 prime or composite?

- Only two factors → 1 and 11
- So, it is prime

✔ Answer:
- Factors: 1, 11
- 11 is a prime number

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## c. Number: 16

Step 1: List all factors of 16

Find pairs that multiply to 16:
- 1 × 16 = 16 → 1, 16
- 2 × 8 = 16 → 2, 8
- 4 × 4 = 16 → 4 (only count once)

✔ Factors of 16: 1, 2, 4, 8, 16

Step 2: Is 16 prime or composite?

- More than two factors → 5 factors
- So, it is composite

✔ Answer:
- Factors: 1, 2, 4, 8, 16
- 16 is a composite number

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## d. Number: 23

Step 1: List all factors of 23

Check multiplication pairs:
- 1 × 23 = 23 → 1, 23
- 2: 23 ÷ 2 = 11.5 → not whole
- 3: 23 ÷ 3 ≈ 7.66 → no
- 4: 23 ÷ 4 = 5.75 → no
- ...
- Up to 22 — none divide 23 evenly

✔ Factors of 23: 1, 23

Step 2: Is 23 prime or composite?

- Only two factors → 1 and 23
- So, it is prime

✔ Answer:
- Factors: 1, 23
- 23 is a prime number

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## ✔ Final Answers:

a.
- Factors of 4: 1, 2, 4
- 4 is composite

b.
- Factors of 11: 1, 11
- 11 is prime

c.
- Factors of 16: 1, 2, 4, 8, 16
- 16 is composite

d.
- Factors of 23: 1, 23
- 23 is prime

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This matches the definitions on the worksheet perfectly! Prime = exactly 2 factors; Composite = more than 2 factors.