Using factor tree, prime factorise the following:
36

Answer

To prime factorize the number 36 using a factor tree, we can follow these steps:

### Step-by-Step Solution:

1. **Start with the number 36**:
- We will create a factor tree starting with the number 36 at the top.

2. **Find two factors of 36**:
- We can divide 36 into two factors. A simple choice is 2 and 18 because \( 2 \times 18 = 36 \).
- Write this down:
```
36
/ \
2 18
```

3. **Factor 18 further**:
- Now, we need to factor 18. We can divide 18 into 2 and 9 since \( 2 \times 9 = 18 \).
- Update the tree:
```
36
/ \
2 18
/ \
2 9
```

4. **Factor 9 further**:
- Next, we factor 9. The factors of 9 are 3 and 3 because \( 3 \times 3 = 9 \).
- Update the tree:
```
36
/ \
2 18
/ \
2 9
/ \
3 3
```

5. **Identify all prime factors**:
- Now, we can see all the prime factors in the tree. The prime factors of 36 are 2, 2, 3, and 3.
- We can express this as:
\[ 36 = 2^2 \times 3^2 \]

### Final Answer:
The prime factorization of 36 is \( 2^2 \times 3^2 \).

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