`325` can be expressed as a product of its primes as

Options

A. `5^(2)xx 7`
B. `5^(2) xx 13`
C. `5 xx 13`
D. `2 xx 3^(2)xx 5^(2)`

Explanation

To express the number 325 as a product of its prime factors, we will follow these steps:

### Step 1: Start with the number 325
We need to factorize 325 into its prime components.

### Step 2: Divide by the smallest prime number
The smallest prime number is 2, but since 325 is odd, we will try the next smallest prime, which is 3.

325 is not divisible by 3 (since 3 + 2 + 5 = 10, which is not divisible by 3).

Next, we try dividing by 5.

### Step 3: Divide by 5
325 ÷ 5 = 65

So, we have:
\[ 325 = 5 \times 65 \]

### Step 4: Factor 65
Now, we need to factor 65. We can again try dividing by 5.

65 ÷ 5 = 13

So, we have:
\[ 65 = 5 \times 13 \]

### Step 5: Combine the factors
Now, we can combine all the factors we found:
\[ 325 = 5 \times 5 \times 13 \]

### Step 6: Write in exponential form
We can express \( 5 \times 5 \) as \( 5^2 \):
\[ 325 = 5^2 \times 13 \]

### Final Answer
Thus, the prime factorization of 325 is:
\[ 325 = 5^2 \times 13 \]

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