Prime And Composite Numbers Worksheet - Free Printable

Let's solve each question step by step and explain the reasoning behind the answers.

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Understanding the Concept: Prime vs Composite Numbers

- A prime number is a number greater than 1 that has only two factors: 1 and itself.
- A composite number is a number greater than 1 that has more than two factors (i.e., it can be factorized into smaller numbers other than 1 and itself).

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Question 1: Factorize 30 in 4 different ways

Given:
- $ 30 = 30 \times 1 $
- $ 30 = 15 \times 2 $
- $ 30 = 5 \times 6 $
- $ 30 = 3 \times 10 $

✔ These are all valid factorizations of 30.

Now, answer:

> Can 30 be factorized into two smaller numbers than itself?

✔️ Yes, because we found multiple pairs like (2,15), (3,10), etc., where both numbers are less than 30.

So, what do we call 30?

👉 Since it can be broken down into smaller whole numbers, it is not prime → it is composite.

✔ Answer: composite

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Question 2: Factorize 16 in two different ways

We need to write 16 as a product of two numbers.

Possible factorizations:
- $ 16 = 8 \times 2 $
- $ 16 = 4 \times 4 $
- $ 16 = 16 \times 1 $ (but this uses the number itself)

So, two different ways using smaller numbers:
- $ 16 = 8 \times 2 $
- $ 16 = 4 \times 4 $

> Can 16 be factorized into two smaller numbers than itself?

✔️ Yes — for example, $ 8 \times 2 $, both 8 and 2 are smaller than 16.

So, what do we call 16?

👉 It has more than two factors → composite

✔ Answer:
- $ 16 = 8 \times 2 $
- $ 16 = 4 \times 4 $
- Yes
- composite

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Question 3: Factorize 7

We need to write 7 as a product of two numbers.

Try:
- $ 7 = 7 \times 1 $
- Is there any other pair? Try $ 7 = 2 \times ? $ → no, not a whole number
- $ 7 = 3 \times ? $ → no
- $ 7 = 4 \times ? $ → no

Only possible factorization: $ 7 = 7 \times 1 $

> Can 7 be factorized into two smaller numbers than itself?

✘ No, because the only factors are 1 and 7. There are no two smaller whole numbers (other than 1) that multiply to give 7.

So, what do we call 7?

👉 Only divisible by 1 and itself → Prime

✔ Answer:
- $ 7 = 7 \times 1 $
- No
- Prime

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✔ Final Answers Summary:

#### 1.
- Factorizations:
$ 30 = 30 \times 1 $
$ 30 = 15 \times 2 $
$ 30 = 5 \times 6 $
$ 30 = 3 \times 10 $
- Can 30 be factorized into two smaller numbers? → Yes
- So, 30 is → composite

#### 2.
- $ 16 = 8 \times 2 $
- $ 16 = 4 \times 4 $
- Can 16 be factorized into two smaller numbers? → Yes
- So, 16 is → composite

#### 3.
- $ 7 = 7 \times 1 $
- Can 7 be factorized into two smaller numbers? → No
- So, 7 is → Prime

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💡 Key Takeaway:
- If a number can be written as a product of two numbers both smaller than itself, it’s composite.
- If the only way to write it is $ n \times 1 $, then it’s prime.

✔ All done!