The number 323 has

Options

A. three prime factors
B. five prime factors
C. two prime factors
D. no prime factor

Answer

To determine how many prime factors the number 323 has, we can follow these steps:

### Step 1: Identify the number
The number we are working with is 323.

### Step 2: Find the factors of 323
To find the prime factors, we first need to identify the factors of 323. We can start by checking for divisibility by smaller prime numbers.

### Step 3: Check for divisibility by 2
323 is an odd number, so it is not divisible by 2.

### Step 4: Check for divisibility by 3
To check for divisibility by 3, we can sum the digits of 323 (3 + 2 + 3 = 8). Since 8 is not divisible by 3, 323 is not divisible by 3.

### Step 5: Check for divisibility by 5
323 does not end in 0 or 5, so it is not divisible by 5.

### Step 6: Check for divisibility by 7
Dividing 323 by 7 gives approximately 46.14, which means 323 is not divisible by 7.

### Step 7: Check for divisibility by 11
Dividing 323 by 11 gives approximately 29.36, which means 323 is not divisible by 11.

### Step 8: Check for divisibility by 17
Dividing 323 by 17 gives exactly 19 (323 ÷ 17 = 19). Thus, we have found that 323 can be factored into 17 and 19.

### Step 9: Verify if the factors are prime
Now we need to check if both 17 and 19 are prime numbers.
- 17 is a prime number (it has no divisors other than 1 and itself).
- 19 is also a prime number (it has no divisors other than 1 and itself).

### Step 10: Conclusion
Since we have found that 323 can be expressed as the product of the prime numbers 17 and 19, we conclude that the number of prime factors of 323 is 2.

### Final Answer
The number 323 has 2 prime factors: 17 and 19.

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