325 can be expressed as a product of its primes as

Options

A. `5^(2)xx7`
B. `5^(2)xx13`
C. `5xx13^(2)`
D. `2xx3^(2)xx5^(2)`

Answer

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

### Step 1: Identify the number
We start with the number 325.

### Step 2: Check for divisibility by the smallest prime number
The smallest prime number is 2. Since 325 is odd, it is not divisible by 2.

### Step 3: Check for divisibility by the next prime number, which is 3
To check if 325 is divisible by 3, we can add the digits of 325 (3 + 2 + 5 = 10). Since 10 is not divisible by 3, 325 is not divisible by 3.

### Step 4: Check for divisibility by the next prime number, which is 5
The last digit of 325 is 5, which means it is divisible by 5.
So, we divide 325 by 5:
\[ 325 \div 5 = 65 \]

### Step 5: Factor 65
Now we need to factor 65. We check for divisibility by the smallest prime numbers again.
- It is not divisible by 2 (since it is odd).
- It is not divisible by 3 (since 6 + 5 = 11, which is not divisible by 3).
- It is divisible by 5 (last digit is 5):
\[ 65 \div 5 = 13 \]

### Step 6: Factor 13
Now we have 13. We check if 13 is a prime number. Since 13 has no divisors other than 1 and itself, it is a prime number.

### Step 7: Write the complete factorization
Now we can write the complete factorization of 325:
\[ 325 = 5 \times 5 \times 13 \]
This can also be expressed as:
\[ 325 = 5^2 \times 13 \]

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

---