Prime factorization of $$$4432$$$

Find the prime factorization of $$$4432$$$.

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

Determine whether $$$4432$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4432$$$ by $$${\color{green}2}$$$: $$$\frac{4432}{2} = {\color{red}2216}$$$.

Determine whether $$$2216$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2216$$$ by $$${\color{green}2}$$$: $$$\frac{2216}{2} = {\color{red}1108}$$$.

Determine whether $$$1108$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1108$$$ by $$${\color{green}2}$$$: $$$\frac{1108}{2} = {\color{red}554}$$$.

Determine whether $$$554$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$554$$$ by $$${\color{green}2}$$$: $$$\frac{554}{2} = {\color{red}277}$$$.

The prime number $$${\color{green}277}$$$ has no other factors then $$$1$$$ and $$${\color{green}277}$$$: $$$\frac{277}{277} = {\color{red}1}$$$.

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: $$$4432 = 2^{4} \cdot 277$$$.

The prime factorization is $$$4432 = 2^{4} \cdot 277$$$A.