Prime factorization of $$$3852$$$

Find the prime factorization of $$$3852$$$.

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

Determine whether $$$3852$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3852$$$ by $$${\color{green}2}$$$: $$$\frac{3852}{2} = {\color{red}1926}$$$.

Determine whether $$$1926$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1926$$$ by $$${\color{green}2}$$$: $$$\frac{1926}{2} = {\color{red}963}$$$.

Determine whether $$$963$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$963$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$963$$$ by $$${\color{green}3}$$$: $$$\frac{963}{3} = {\color{red}321}$$$.

Determine whether $$$321$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$321$$$ by $$${\color{green}3}$$$: $$$\frac{321}{3} = {\color{red}107}$$$.

The prime number $$${\color{green}107}$$$ has no other factors then $$$1$$$ and $$${\color{green}107}$$$: $$$\frac{107}{107} = {\color{red}1}$$$.

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: $$$3852 = 2^{2} \cdot 3^{2} \cdot 107$$$.

The prime factorization is $$$3852 = 2^{2} \cdot 3^{2} \cdot 107$$$A.