Find the prime factors of the following:
`120`

Answer

To find the prime factors of 120, we can follow these steps:

### Step 1: Start with the number 120
We need to factor 120 into its prime components.

### Step 2: Divide by the smallest prime number
The smallest prime number is 2. Since 120 is even, we can divide it by 2:
\[ 120 \div 2 = 60 \]

### Step 3: Repeat the process
Now, we take 60 and divide it by 2 again:
\[ 60 \div 2 = 30 \]

### Step 4: Continue dividing by 2
Next, we take 30 and divide it by 2 once more:
\[ 30 \div 2 = 15 \]

### Step 5: Now, divide by the next smallest prime number
15 is not divisible by 2 (since it is odd), so we move to the next smallest prime number, which is 3. We divide 15 by 3:
\[ 15 \div 3 = 5 \]

### Step 6: Finally, we have a prime number
Now we have 5, which is a prime number itself.

### Step 7: Collect all the prime factors
Now we can list all the prime factors we found:
- From the divisions, we used 2 three times (2, 2, 2)
- We used 3 once
- We used 5 once

Thus, the prime factorization of 120 is:
\[ 120 = 2^3 \times 3^1 \times 5^1 \]

### Final Answer:
The prime factors of 120 are \( 2, 3, \) and \( 5 \).

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