# Prime factorization of $3036$

The calculator will find the prime factorization of $3036$, with steps shown.

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Find the prime factorization of $3036$.

### Solution

Start with the number $2$.

Determine whether $3036$ is divisible by $2$.

It is divisible, thus, divide $3036$ by ${\color{green}2}$: $\frac{3036}{2} = {\color{red}1518}$.

Determine whether $1518$ is divisible by $2$.

It is divisible, thus, divide $1518$ by ${\color{green}2}$: $\frac{1518}{2} = {\color{red}759}$.

Determine whether $759$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $759$ is divisible by $3$.

It is divisible, thus, divide $759$ by ${\color{green}3}$: $\frac{759}{3} = {\color{red}253}$.

Determine whether $253$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $253$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $253$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $253$ is divisible by $11$.

It is divisible, thus, divide $253$ by ${\color{green}11}$: $\frac{253}{11} = {\color{red}23}$.

The prime number ${\color{green}23}$ has no other factors then $1$ and ${\color{green}23}$: $\frac{23}{23} = {\color{red}1}$.

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: $3036 = 2^{2} \cdot 3 \cdot 11 \cdot 23$.

The prime factorization is $3036 = 2^{2} \cdot 3 \cdot 11 \cdot 23$A.