Prime factorization of 36 and 54 using factor trees.

The image shows the prime factorization of two numbers: 36 and 54, using a factor tree method.

Let’s go through each step carefully and explain the solution.

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🔹 Prime Factorization of 36

We start with 36:

```
36
/ \
4 9
/ \ / \
2 2 3 3
```

- 36 is broken down into 4 × 9
- 4 = 2 × 2
- 9 = 3 × 3

So, combining all the prime factors:
> 36 = 2 × 2 × 3 × 3
> or in exponential form:
> 36 = 2² × 3²

---

🔹 Prime Factorization of 54

Now for 54:

```
54
/ \
6 9
/ \ / \
2 3 3 3
```

- 54 is broken down into 6 × 9
- 6 = 2 × 3
- 9 = 3 × 3

So, combining all the prime factors:
> 54 = 2 × 3 × 3 × 3
> or in exponential form:
> 54 = 2¹ × 3³

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✔ Final Answer:

- 36 = 2² × 3²
- 54 = 2¹ × 3³

These are the prime factorizations of the numbers shown in the image.

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📌 Additional Insight (Optional)

If you were asked to find the GCF (Greatest Common Factor) or LCM (Least Common Multiple) of 36 and 54, here's how:

#### GCF:
Take the lowest power of common primes:
- Common primes: 2 and 3
- Min(2², 2¹) = 2¹
- Min(3², 3³) = 3²
- So, GCF = 2 × 3² = 2 × 9 = 18

#### LCM:
Take the highest power of all primes:
- Max(2², 2¹) = 2²
- Max(3², 3³) = 3³
- So, LCM = 2² × 3³ = 4 × 27 = 108

But since your task was just to solve the factor trees, the main answer is:

> ✔ 36 = 2 × 2 × 3 × 3
> ✔ 54 = 2 × 3 × 3 × 3

This matches what's shown in the image. ✔️