Express 120 as the product of prime factors.

Answer

To express 120 as the product of its prime factors, we will perform prime factorization step by step.

### Step 1: Start with the number 120
We begin with the number 120.

### Step 2: Check for divisibility by the smallest prime number (2)
Since 120 is an even number (it ends with 0), it is divisible by 2.

\[ 120 \div 2 = 60 \]

### Step 3: Continue dividing by 2
Now we take the quotient 60 and check if it is divisible by 2 again.

\[ 60 \div 2 = 30 \]

### Step 4: Divide by 2 once more
Next, we take 30 and divide by 2 again.

\[ 30 \div 2 = 15 \]

### Step 5: Check for the next prime number (3)
Now we have 15, which is not divisible by 2. We check for the next prime number, which is 3.

\[ 15 \div 3 = 5 \]

### Step 6: Divide by the last prime number (5)
Finally, we take 5, which is a prime number itself.

\[ 5 \div 5 = 1 \]

### Step 7: Collect all the prime factors
Now we can collect all the prime factors we used in the division process:

- We divided by 2 three times (2, 2, 2)
- We divided by 3 once
- We divided by 5 once

### Final Expression
Thus, we can express 120 as the product of its prime factors:

\[ 120 = 2^3 \times 3^1 \times 5^1 \]

### Summary
The prime factorization of 120 is \( 2^3 \times 3^1 \times 5^1 \).

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