Prime factorization of $$$1052$$$

Find the prime factorization of $$$1052$$$.

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

Determine whether $$$1052$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1052$$$ by $$${\color{green}2}$$$: $$$\frac{1052}{2} = {\color{red}526}$$$.

Determine whether $$$526$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$526$$$ by $$${\color{green}2}$$$: $$$\frac{526}{2} = {\color{red}263}$$$.

The prime number $$${\color{green}263}$$$ has no other factors then $$$1$$$ and $$${\color{green}263}$$$: $$$\frac{263}{263} = {\color{red}1}$$$.

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: $$$1052 = 2^{2} \cdot 263$$$.

The prime factorization is $$$1052 = 2^{2} \cdot 263$$$A.