Prime factorization of $$$4552$$$

Find the prime factorization of $$$4552$$$.

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

Determine whether $$$4552$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4552$$$ by $$${\color{green}2}$$$: $$$\frac{4552}{2} = {\color{red}2276}$$$.

Determine whether $$$2276$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2276$$$ by $$${\color{green}2}$$$: $$$\frac{2276}{2} = {\color{red}1138}$$$.

Determine whether $$$1138$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1138$$$ by $$${\color{green}2}$$$: $$$\frac{1138}{2} = {\color{red}569}$$$.

The prime number $$${\color{green}569}$$$ has no other factors then $$$1$$$ and $$${\color{green}569}$$$: $$$\frac{569}{569} = {\color{red}1}$$$.

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: $$$4552 = 2^{3} \cdot 569$$$.

The prime factorization is $$$4552 = 2^{3} \cdot 569$$$A.