Students can practice breaking down composite numbers into their prime factors using this structured division worksheet.

Prime Numbers Worksheet 3 featuring prime factorization exercises where students fill in missing numbers.

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Let's solve the Prime Factorization worksheet step by step. The goal is to fill in the missing numbers to complete the prime factorization of each number using a factor tree method.

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🔍 Understanding Prime Factorization

Prime factorization breaks down a number into its prime factors (numbers divisible only by 1 and themselves). We divide the number by prime numbers until we reach 1.

We'll go through each problem one by one.

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✔ Example Given:

```
32
/ \
2 16
/ \
2 8
/ \
2 4
/ \
2 2
```

So, 32 = 2 × 2 × 2 × 2 × 2 = 2⁵

Now let’s solve each blank.

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1. 72

```
72
/ \
2 36
/ \
2 18
/ \
2 9
/ \
3 3
```

So:
- 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

Fill in:
- First branch: 2 and 36
- Second: 2 and 18
- Third: 2 and 9
- Fourth: 3 and 3

Answer at bottom: 2 × 2 × 2 × 3 × 3 = 72

✔ Done.

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2. 120

```
120
/ \
2 60
/ \
2 30
/ \
2 15
/ \
3 5
```

So:
- 120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5

Fill in:
- 2 and 60
- 2 and 30
- 2 and 15
- 3 and 5

Answer: 2 × 2 × 2 × 3 × 5 = 120

✔ Done.

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3. 252

```
252
/ \
2 126
/ \
2 63
/ \
3 21
/ \
3 7
```

So:
- 252 = 2 × 2 × 3 × 3 × 7 = 2² × 3² × 7

Fill in:
- 2 and 126
- 2 and 63
- 3 and 21
- 3 and 7

Answer: 2 × 2 × 3 × 3 × 7 = 252

✔ Done.

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4. 168

```
168
/ \
2 84
/ \
2 42
/ \
2 21
/ \
3 7
```

So:
- 168 = 2 × 2 × 2 × 3 × 7 = 2³ × 3 × 7

Fill in:
- 2 and 84
- 2 and 42
- 2 and 21
- 3 and 7

Answer: 2 × 2 × 2 × 3 × 7 = 168

✔ Done.

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5. 420

```
420
/ \
2 210
/ \
2 105
/ \
3 35
/ \
5 7
```

So:
- 420 = 2 × 2 × 3 × 5 × 7 = 2² × 3 × 5 × 7

Fill in:
- 2 and 210
- 2 and 105
- 3 and 35
- 5 and 7

Answer: 2 × 2 × 3 × 5 × 7 = 420

✔ Done.

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6. 210

```
210
/ \
2 105
/ \
3 35
/ \
5 7
```

So:
- 210 = 2 × 3 × 5 × 7

Fill in:
- 2 and 105
- 3 and 35
- 5 and 7

Answer: 2 × 3 × 5 × 7 = 210

✔ Done.

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7. 378

```
378
/ \
2 189
/ \
3 63
/ \
3 21
/ \
3 7
```

So:
- 378 = 2 × 3 × 3 × 3 × 7 = 2 × 3³ × 7

Fill in:
- 2 and 189
- 3 and 63
- 3 and 21
- 3 and 7

Answer: 2 × 3 × 3 × 3 × 7 = 378

✔ Done.

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8. 2100

```
2100
/ \
2 1050
/ \
2 525
/ \
3 175
/ \
5 35
/ \
5 7
```

So:
- 2100 = 2 × 2 × 3 × 5 × 5 × 7 = 2² × 3 × 5² × 7

Fill in:
- 2 and 1050
- 2 and 525
- 3 and 175
- 5 and 35
- 5 and 7

Answer: 2 × 2 × 3 × 5 × 5 × 7 = 2100

✔ Done.

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✔ Final Answers Summary:

| Number | Prime Factorization |
|--------|---------------------|
| 72 | 2 × 2 × 2 × 3 × 3 = 72 |
| 120 | 2 × 2 × 2 × 3 × 5 = 120 |
| 252 | 2 × 2 × 3 × 3 × 7 = 252 |
| 168 | 2 × 2 × 2 × 3 × 7 = 168 |
| 420 | 2 × 2 × 3 × 5 × 7 = 420 |
| 210 | 2 × 3 × 5 × 7 = 210 |
| 378 | 2 × 3 × 3 × 3 × 7 = 378 |
| 2100 | 2 × 2 × 3 × 5 × 5 × 7 = 2100 |

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📝 How to Fill In the Worksheet:

For each box:
- Start with the number.
- Divide by smallest prime (usually 2).
- Keep dividing until all are primes.
- Fill in the blanks accordingly.

You can now fill in the worksheet using the above breakdowns.

Let me know if you want this as a printable filled-in version!

Parent Tip: Review the logic above to help your child master the concept of year 5 maths worksheet.

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