Prime factorization worksheet for students to practice finding prime factors of numbers.

Let's solve each problem by finding the prime factorization of each number. Prime factorization means expressing a number as a product of prime numbers.

We'll go through each number one by one:

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1) 26
- 26 ÷ 2 = 13
- 13 is a prime number
✔ 2 × 13

2) 52
- 52 ÷ 2 = 26
- 26 ÷ 2 = 13
- 13 is prime
✔ 2² × 13

3) 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
✔ 2² × 3²

4) 51
- 51 ÷ 3 = 17
- 17 is prime
✔ 3 × 17

5) 54
- 54 ÷ 2 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
✔ 2 × 3³

6) 40
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 is prime
✔ 2³ × 5

7) 33
- 33 ÷ 3 = 11
- 11 is prime
✔ 3 × 11

8) 44
- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
- 11 is prime
✔ 2² × 11

9) 64
- 64 ÷ 2 = 32
- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
✔ 2⁶

10) 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 is prime
✔ 2 × 3 × 5

11) 22
- 22 ÷ 2 = 11
- 11 is prime
✔ 2 × 11

12) 42
- 42 ÷ 2 = 21
- 21 ÷ 3 = 7
- 7 is prime
✔ 2 × 3 × 7

13) 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1
✔ 2⁴

14) 18
- 18 ÷ 2 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
✔ 2 × 3²

15) 77
- 77 ÷ 7 = 11
- 11 is prime
✔ 7 × 11

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✔ Final Answers:

1) 26 → 2 × 13
2) 52 → 2² × 13
3) 36 → 2² × 3²
4) 51 → 3 × 17
5) 54 → 2 × 3³
6) 40 → 2³ × 5
7) 33 → 3 × 11
8) 44 → 2² × 11
9) 64 → 2⁶
10) 30 → 2 × 3 × 5
11) 22 → 2 × 11
12) 42 → 2 × 3 × 7
13) 16 → 2⁴
14) 18 → 2 × 3²
15) 77 → 7 × 11

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You can now fill these in on the worksheet! Let me know if you'd like it formatted for printing or need help understanding any step.