Prime factorization of $$$1362$$$

Find the prime factorization of $$$1362$$$.

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

Determine whether $$$1362$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1362$$$ by $$${\color{green}2}$$$: $$$\frac{1362}{2} = {\color{red}681}$$$.

Determine whether $$$681$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$681$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$681$$$ by $$${\color{green}3}$$$: $$$\frac{681}{3} = {\color{red}227}$$$.

The prime number $$${\color{green}227}$$$ has no other factors then $$$1$$$ and $$${\color{green}227}$$$: $$$\frac{227}{227} = {\color{red}1}$$$.

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: $$$1362 = 2 \cdot 3 \cdot 227$$$.

The prime factorization is $$$1362 = 2 \cdot 3 \cdot 227$$$A.