Prime factorization of $$$592$$$

Find the prime factorization of $$$592$$$.

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

Determine whether $$$592$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$592$$$ by $$${\color{green}2}$$$: $$$\frac{592}{2} = {\color{red}296}$$$.

Determine whether $$$296$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$296$$$ by $$${\color{green}2}$$$: $$$\frac{296}{2} = {\color{red}148}$$$.

Determine whether $$$148$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$148$$$ by $$${\color{green}2}$$$: $$$\frac{148}{2} = {\color{red}74}$$$.

Determine whether $$$74$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$74$$$ by $$${\color{green}2}$$$: $$$\frac{74}{2} = {\color{red}37}$$$.

The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.

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: $$$592 = 2^{4} \cdot 37$$$.

The prime factorization is $$$592 = 2^{4} \cdot 37$$$A.