The prime factorization of 399 can be found by dividing the number by its smallest prime factors until we can no longer divide.
First, we check if 399 is divisible by 2. Since 399 is an odd number, it’s not. Next, we try dividing by 3:
- 399 ÷ 3 = 133
So, we have our first prime factor: 3. Next, we continue with 133. We check 133 for divisibility by the next prime numbers.
- 133 is not even, so we try 3 again, but it doesn’t work.
- Then we check 5, which also doesn’t work.
- Next, we try 7, and 133 ÷ 7 is not a whole number either.
- Now checking 11, we find:
- 133 ÷ 7 = 19, so now we have our second prime factor: 7.
Finally, we see that 19 is also a prime number. Therefore, the complete prime factorization of 399 is:
3 × 7 × 19
In summary, the prime factorization of 399 is derived by breaking it down into its prime components—3, 7, and 19—showing how each number contributes to the product that gives us 399.