# Prime factorization of $2814$

The calculator will find the prime factorization of $2814$, with steps shown.

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Find the prime factorization of $2814$.

### Solution

Start with the number $2$.

Determine whether $2814$ is divisible by $2$.

It is divisible, thus, divide $2814$ by ${\color{green}2}$: $\frac{2814}{2} = {\color{red}1407}$.

Determine whether $1407$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1407$ is divisible by $3$.

It is divisible, thus, divide $1407$ by ${\color{green}3}$: $\frac{1407}{3} = {\color{red}469}$.

Determine whether $469$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $469$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $469$ is divisible by $7$.

It is divisible, thus, divide $469$ by ${\color{green}7}$: $\frac{469}{7} = {\color{red}67}$.

The prime number ${\color{green}67}$ has no other factors then $1$ and ${\color{green}67}$: $\frac{67}{67} = {\color{red}1}$.

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: $2814 = 2 \cdot 3 \cdot 7 \cdot 67$.

The prime factorization is $2814 = 2 \cdot 3 \cdot 7 \cdot 67$A.