# Prime factorization of $4086$

The calculator will find the prime factorization of $4086$, with steps shown.

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Find the prime factorization of $4086$.

### Solution

Start with the number $2$.

Determine whether $4086$ is divisible by $2$.

It is divisible, thus, divide $4086$ by ${\color{green}2}$: $\frac{4086}{2} = {\color{red}2043}$.

Determine whether $2043$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2043$ is divisible by $3$.

It is divisible, thus, divide $2043$ by ${\color{green}3}$: $\frac{2043}{3} = {\color{red}681}$.

Determine whether $681$ is divisible by $3$.

It is divisible, thus, divide $681$ by ${\color{green}3}$: $\frac{681}{3} = {\color{red}227}$.

The prime number ${\color{green}227}$ has no other factors then $1$ and ${\color{green}227}$: $\frac{227}{227} = {\color{red}1}$.

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: $4086 = 2 \cdot 3^{2} \cdot 227$.

The prime factorization is $4086 = 2 \cdot 3^{2} \cdot 227$A.