Prime factorization of $$$4252$$$

Find the prime factorization of $$$4252$$$.

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

Determine whether $$$4252$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4252$$$ by $$${\color{green}2}$$$: $$$\frac{4252}{2} = {\color{red}2126}$$$.

Determine whether $$$2126$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2126$$$ by $$${\color{green}2}$$$: $$$\frac{2126}{2} = {\color{red}1063}$$$.

The prime number $$${\color{green}1063}$$$ has no other factors then $$$1$$$ and $$${\color{green}1063}$$$: $$$\frac{1063}{1063} = {\color{red}1}$$$.

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: $$$4252 = 2^{2} \cdot 1063$$$.

The prime factorization is $$$4252 = 2^{2} \cdot 1063$$$A.