Prime factorization of $$$1398$$$

Find the prime factorization of $$$1398$$$.

Start with the number $$$2$$$.

Determine whether $$$1398$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1398$$$ by $$${\color{green}2}$$$: $$$\frac{1398}{2} = {\color{red}699}$$$.

Determine whether $$$699$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$699$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$699$$$ by $$${\color{green}3}$$$: $$$\frac{699}{3} = {\color{red}233}$$$.

The prime number $$${\color{green}233}$$$ has no other factors then $$$1$$$ and $$${\color{green}233}$$$: $$$\frac{233}{233} = {\color{red}1}$$$.

Since we have obtained $$$1$$$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$1398 = 2 \cdot 3 \cdot 233$$$.

The prime factorization is $$$1398 = 2 \cdot 3 \cdot 233$$$A.