Prime factorization of $$$1852$$$

Find the prime factorization of $$$1852$$$.

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

Determine whether $$$1852$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1852$$$ by $$${\color{green}2}$$$: $$$\frac{1852}{2} = {\color{red}926}$$$.

Determine whether $$$926$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$926$$$ by $$${\color{green}2}$$$: $$$\frac{926}{2} = {\color{red}463}$$$.

The prime number $$${\color{green}463}$$$ has no other factors then $$$1$$$ and $$${\color{green}463}$$$: $$$\frac{463}{463} = {\color{red}1}$$$.

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: $$$1852 = 2^{2} \cdot 463$$$.

The prime factorization is $$$1852 = 2^{2} \cdot 463$$$A.