# Prime factorization of $3852$

The calculator will find the prime factorization of $3852$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $3852$.

### Solution

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.