Prime Factorization | Worksheet - Free Printable

Let's solve the Prime Factorization worksheet step by step. The goal is to find the prime factorization of each given number, breaking it down into a product of prime numbers. We’ll use factor trees or repeated division by primes, and write the final answer in exponential form if possible.

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🔷 Understanding Prime Factorization:

- A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
- Prime factorization means expressing a number as a product of prime numbers.
- We can use a factor tree method: divide the number by the smallest prime until all factors are prime.

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We’ll go through each number one by one.

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✔ Example Given (24):

They show:
```
24
/ \
6 4
/ \ / \
3 2 2 2
```

So, the prime factors are:
2 × 2 × 2 × 3 → which is 2³ × 3

✔ Correct.

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Now let’s do the rest:

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1. 50

Start dividing by smallest prime:
- 50 ÷ 2 = 25 → 2 is prime
- 25 ÷ 5 = 5 → 5 is prime
- 5 ÷ 5 = 1

So, prime factors: 2 × 5 × 5 → 2 × 5²

✔ Answer: 2 × 5²

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2. 56

- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7 → 7 is prime

So, prime factors: 2 × 2 × 2 × 7 → 2³ × 7

✔ Answer: 2³ × 7

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3. 42

- 42 ÷ 2 = 21
- 21 ÷ 3 = 7 → 7 is prime

So, prime factors: 2 × 3 × 7

✔ Answer: 2 × 3 × 7

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4. 27

- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1

So, prime factors: 3 × 3 × 3 → 3³

✔ Answer: 3³

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5. 66

- 66 ÷ 2 = 33
- 33 ÷ 3 = 11 → 11 is prime

So, prime factors: 2 × 3 × 11

✔ Answer: 2 × 3 × 11

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6. 43

- 43 is a prime number (only divisible by 1 and 43)

✔ Answer: 43 (already prime)

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7. 48

- 48 ÷ 2 = 24
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3 → 3 is prime

So, prime factors: 2 × 2 × 2 × 2 × 3 → 2⁴ × 3

✔ Answer: 2⁴ × 3

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8. 70

- 70 ÷ 2 = 35
- 35 ÷ 5 = 7 → 7 is prime

So, prime factors: 2 × 5 × 7

✔ Answer: 2 × 5 × 7

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9. 48 — already done above

Wait! 48 appears twice? Let's check:

Looking at the image layout:
- Row 1: 50, 56
- Row 2: 42, 27
- Row 3: 66, 43
- Row 4: 48, 70
- Row 5: 48, 70 ← Wait, 48 and 70 again?

But actually, looking at the structure:

It seems like there are two rows of numbers:
- First row: 50, 56
- Second: 42, 27
- Third: 66, 43
- Fourth: 48, 70
- Fifth: 48, 70 → possibly typo or repeat?

But likely, the last two boxes are meant to be separate entries. Let’s assume they are:
- 48 (again) and 70 (again), but maybe it's a mistake.

But since both are already solved, we'll just list them again.

Wait — actually, in the image, the bottom row says:
> 48 70

So only one instance of each.

But earlier we did 48 and 70 already.

So now, let’s double-check all:

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Final Answers:

| Number | Prime Factorization |
|--------|---------------------|
| 50 | 2 × 5² |
| 56 | 2³ × 7 |
| 42 | 2 × 3 × 7 |
| 27 | 3³ |
| 66 | 2 × 3 × 11 |
| 43 | 43 (prime) |
| 48 | 2⁴ × 3 |
| 70 | 2 × 5 × 7 |

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✔ Completed Worksheet:

Now fill in the boxes:

- 50: $ 2 \times 5^2 $
- 56: $ 2^3 \times 7 $
- 42: $ 2 \times 3 \times 7 $
- 27: $ 3^3 $
- 66: $ 2 \times 3 \times 11 $
- 43: $ 43 $
- 48: $ 2^4 \times 3 $
- 70: $ 2 \times 5 \times 7 $

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📌 Tips for Students:

- Always start with the smallest prime (2).
- If the number is odd, skip 2 and try 3, 5, 7, etc.
- Use divisibility rules:
- Divisible by 2 → ends in even digit
- By 3 → sum of digits divisible by 3
- By 5 → ends in 0 or 5
- Keep dividing until all factors are prime.
- Write the final answer in order from least to greatest, using exponents when possible.

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✔ All problems solved!

Let me know if you'd like a printable version or visual factor trees!