Prime factorization of $$$692$$$

Find the prime factorization of $$$692$$$.

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

Determine whether $$$692$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$692$$$ by $$${\color{green}2}$$$: $$$\frac{692}{2} = {\color{red}346}$$$.

Determine whether $$$346$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$346$$$ by $$${\color{green}2}$$$: $$$\frac{346}{2} = {\color{red}173}$$$.

The prime number $$${\color{green}173}$$$ has no other factors then $$$1$$$ and $$${\color{green}173}$$$: $$$\frac{173}{173} = {\color{red}1}$$$.

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: $$$692 = 2^{2} \cdot 173$$$.

The prime factorization is $$$692 = 2^{2} \cdot 173$$$A.