Prime Factorization Worksheet page - Free Printable

To solve the problem of finding the prime factorization for each number, we need to break down each number into its prime factors. Here's the step-by-step solution for each number:

Prime Factorization Steps:

1. Start with the smallest prime number (2) and see if it divides the given number.
2. If it does, divide the number by 2 and continue dividing by 2 until it no longer divides evenly.
3. Move on to the next smallest prime number (3) and repeat the process.
4. Continue with the next prime numbers (5, 7, 11, etc.) until the number is fully factored into primes.

Solutions:

1. 33
- 33 ÷ 3 = 11
- 11 is a prime number.
- Prime factorization: \( 33 = 3 \times 11 \)

2. 25
- 25 ÷ 5 = 5
- 5 is a prime number.
- Prime factorization: \( 25 = 5 \times 5 \) or \( 5^2 \)

3. 14
- 14 ÷ 2 = 7
- 7 is a prime number.
- Prime factorization: \( 14 = 2 \times 7 \)

4. 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 is a prime number.
- Prime factorization: \( 8 = 2 \times 2 \times 2 \) or \( 2^3 \)

5. 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 is a prime number.
- Prime factorization: \( 20 = 2 \times 2 \times 5 \) or \( 2^2 \times 5 \)

6. 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 is a prime number.
- Prime factorization: \( 30 = 2 \times 3 \times 5 \)

7. 18
- 18 ÷ 2 = 9
- 9 ÷ 3 = 3
- 3 is a prime number.
- Prime factorization: \( 18 = 2 \times 3 \times 3 \) or \( 2 \times 3^2 \)

8. 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 is a prime number.
- Prime factorization: \( 24 = 2 \times 2 \times 2 \times 3 \) or \( 2^3 \times 3 \)

9. 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 is a prime number.
- Prime factorization: \( 27 = 3 \times 3 \times 3 \) or \( 3^3 \)

10. 44
- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
- 11 is a prime number.
- Prime factorization: \( 44 = 2 \times 2 \times 11 \) or \( 2^2 \times 11 \)

11. 50
- 50 ÷ 2 = 25
- 25 ÷ 5 = 5
- 5 is a prime number.
- Prime factorization: \( 50 = 2 \times 5 \times 5 \) or \( 2 \times 5^2 \)

12. 35
- 35 ÷ 5 = 7
- 7 is a prime number.
- Prime factorization: \( 35 = 5 \times 7 \)

13. 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 is a prime number.
- Prime factorization: \( 45 = 3 \times 3 \times 5 \) or \( 3^2 \times 5 \)

14. 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 is a prime number.
- Prime factorization: \( 60 = 2 \times 2 \times 3 \times 5 \) or \( 2^2 \times 3 \times 5 \)

15. 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 is a prime number.
- Prime factorization: \( 32 = 2 \times 2 \times 2 \times 2 \times 2 \) or \( 2^5 \)

16. 42
- 42 ÷ 2 = 21
- 21 ÷ 3 = 7
- 7 is a prime number.
- Prime factorization: \( 42 = 2 \times 3 \times 7 \)

17. 48
- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 is a prime number.
- Prime factorization: \( 48 = 2 \times 2 \times 2 \times 2 \times 3 \) or \( 2^4 \times 3 \)

18. 54
- 54 ÷ 2 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 is a prime number.
- Prime factorization: \( 54 = 2 \times 3 \times 3 \times 3 \) or \( 2 \times 3^3 \)

19. 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
- 9 ÷ 3 = 3
- 3 is a prime number.
- Prime factorization: \( 36 = 2 \times 2 \times 3 \times 3 \) or \( 2^2 \times 3^2 \)

20. 80
- 80 ÷ 2 = 40
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 is a prime number.
- Prime factorization: \( 80 = 2 \times 2 \times 2 \times 2 \times 5 \) or \( 2^4 \times 5 \)

Final Answer:

\[
\boxed{
\begin{aligned}
1) & \quad 33 = 3 \times 11 \\
2) & \quad 25 = 5 \times 5 \\
3) & \quad 14 = 2 \times 7 \\
4) & \quad 8 = 2 \times 2 \times 2 \\
5) & \quad 20 = 2 \times 2 \times 5 \\
6) & \quad 30 = 2 \times 3 \times 5 \\
7) & \quad 18 = 2 \times 3 \times 3 \\
8) & \quad 24 = 2 \times 2 \times 2 \times 3 \\
9) & \quad 27 = 3 \times 3 \times 3 \\
10) & \quad 44 = 2 \times 2 \times 11 \\
11) & \quad 50 = 2 \times 5 \times 5 \\
12) & \quad 35 = 5 \times 7 \\
13) & \quad 45 = 3 \times 3 \times 5 \\
14) & \quad 60 = 2 \times 2 \times 3 \times 5 \\
15) & \quad 32 = 2 \times 2 \times 2 \times 2 \times 2 \\
16) & \quad 42 = 2 \times 3 \times 7 \\
17) & \quad 48 = 2 \times 2 \times 2 \times 2 \times 3 \\
18) & \quad 54 = 2 \times 3 \times 3 \times 3 \\
19) & \quad 36 = 2 \times 2 \times 3 \times 3 \\
20) & \quad 80 = 2 \times 2 \times 2 \times 2 \times 5 \\
\end{aligned}
}
\]