Factor Trees Worksheet | Maths Teaching Resource | Year 5-6 - Free Printable

To solve the problem, we need to factorize each given number into its prime factors using a factor tree. Let's go through each number step by step.

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1. Factor Tree for 54

#### Step 1: Start with 54.
- Find two numbers that multiply to give 54. For example, \(54 = 6 \times 9\).

#### Step 2: Factor 6 and 9 further.
- \(6 = 2 \times 3\)
- \(9 = 3 \times 3\)

#### Step 3: Write the prime factors.
- The prime factors of 54 are \(2, 3, 3, 3\).

#### Factor Tree:
```
54
/ \
6 9
/ \ / \
2 3 3 3
```

#### Apples (Prime Factors):
- \(2, 3, 3, 3\)

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2. Factor Tree for 81

#### Step 1: Start with 81.
- Find two numbers that multiply to give 81. For example, \(81 = 9 \times 9\).

#### Step 2: Factor 9 further.
- \(9 = 3 \times 3\)
- So, \(81 = 9 \times 9 = (3 \times 3) \times (3 \times 3)\).

#### Step 3: Write the prime factors.
- The prime factors of 81 are \(3, 3, 3, 3\).

#### Factor Tree:
```
81
/ \
9 9
/ \ / \
3 3 3 3
```

#### Apples (Prime Factors):
- \(3, 3, 3, 3\)

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3. Factor Tree for 72

#### Step 1: Start with 72.
- Find two numbers that multiply to give 72. For example, \(72 = 8 \times 9\).

#### Step 2: Factor 8 and 9 further.
- \(8 = 2 \times 4\) and \(4 = 2 \times 2\), so \(8 = 2 \times 2 \times 2\).
- \(9 = 3 \times 3\).

#### Step 3: Write the prime factors.
- The prime factors of 72 are \(2, 2, 2, 3, 3\).

#### Factor Tree:
```
72
/ \
8 9
/ \ / \
2 4 3 3
/ \
2 2
```

#### Apples (Prime Factors):
- \(2, 2, 2, 3, 3\)

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4. Factor Tree for 450

#### Step 1: Start with 450.
- Find two numbers that multiply to give 450. For example, \(450 = 50 \times 9\).

#### Step 2: Factor 50 and 9 further.
- \(50 = 10 \times 5\) and \(10 = 2 \times 5\), so \(50 = 2 \times 5 \times 5\).
- \(9 = 3 \times 3\).

#### Step 3: Write the prime factors.
- The prime factors of 450 are \(2, 3, 3, 5, 5\).

#### Factor Tree:
```
450
/ \
50 9
/ \ / \
10 5 3 3
/ \
2 5
```

#### Apples (Prime Factors):
- \(2, 3, 3, 5, 5\)

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Final Answers

1. For 54: \( \boxed{2, 3, 3, 3} \)
2. For 81: \( \boxed{3, 3, 3, 3} \)
3. For 72: \( \boxed{2, 2, 2, 3, 3} \)
4. For 450: \( \boxed{2, 3, 3, 5, 5} \)