Express 75 as the product of prime factors.

Answer

To express 75 as the product of its prime factors, we will follow the process of prime factorization step by step.

### Step 1: Start with the number
We begin with the number 75.

### Step 2: Divide by the smallest prime number
The smallest prime number is 2. Since 75 is odd, it is not divisible by 2. We move to the next smallest prime number, which is 3.

### Step 3: Check divisibility by 3
We divide 75 by 3:
\[ 75 \div 3 = 25 \]
So, we can write:
\[ 75 = 3 \times 25 \]

### Step 4: Factor 25
Now, we need to factor 25. The smallest prime number that can divide 25 is 5.
We divide 25 by 5:
\[ 25 \div 5 = 5 \]
So, we can write:
\[ 25 = 5 \times 5 \]
Thus, we can express 75 as:
\[ 75 = 3 \times 5 \times 5 \]

### Step 5: Write in exponential form
Since 5 is repeated, we can express it in exponential form:
\[ 75 = 3 \times 5^2 \]

### Final Answer
Therefore, the prime factorization of 75 is:
\[ 75 = 3 \times 5^2 \]

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