Find the prime factorization of 360

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To find the **prime factorization** of **360**, we'll break it down into its prime number components step by step.

### Step-by-Step Prime Factorization:

1. **Divide by 2 (the smallest prime number):**
   - $$ 360 \div 2 = 180 $$

2. **Divide by 2 again:**
   - $$ 180 \div 2 = 90 $$

3. **Divide by 2 once more:**
   - $$ 90 \div 2 = 45 $$

4. **Now, 45 is not divisible by 2. Move to the next prime number, which is 3:**
   - $$ 45 \div 3 = 15 $$

5. **Divide by 3 again:**
   - $$ 15 \div 3 = 5 $$

6. **Finally, 5 is a prime number and cannot be divided further by other primes.**

### Putting It All Together:

So, the prime factors of 360 are:
- **2** multiplied by itself **three times** ($$2^3$$)
- **3** multiplied by itself **twice** ($$3^2$$)
- **5** once ($$5^1$$)

### Prime Factorization of 360:
$$ 360 = 2^3 \times 3^2 \times 5 $$

### Verification:

To ensure the factorization is correct:
$$ 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 72 \times 5 = 360 $$

This confirms that the prime factorization of 360 is indeed $$2^3 \times 3^2 \times 5$$.
The prime factorization of 360 is $$2^3 \times 3^2 \times 5$$.

Find the prime factorization of 360

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