Prime factorization of $$$1962$$$

Find the prime factorization of $$$1962$$$.

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

Determine whether $$$1962$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1962$$$ by $$${\color{green}2}$$$: $$$\frac{1962}{2} = {\color{red}981}$$$.

Determine whether $$$981$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$981$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$981$$$ by $$${\color{green}3}$$$: $$$\frac{981}{3} = {\color{red}327}$$$.

Determine whether $$$327$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$327$$$ by $$${\color{green}3}$$$: $$$\frac{327}{3} = {\color{red}109}$$$.

The prime number $$${\color{green}109}$$$ has no other factors then $$$1$$$ and $$${\color{green}109}$$$: $$$\frac{109}{109} = {\color{red}1}$$$.

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: $$$1962 = 2 \cdot 3^{2} \cdot 109$$$.

The prime factorization is $$$1962 = 2 \cdot 3^{2} \cdot 109$$$A.