# Prime factorization of $2812$

The calculator will find the prime factorization of $2812$, with steps shown.

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Find the prime factorization of $2812$.

### Solution

Start with the number $2$.

Determine whether $2812$ is divisible by $2$.

It is divisible, thus, divide $2812$ by ${\color{green}2}$: $\frac{2812}{2} = {\color{red}1406}$.

Determine whether $1406$ is divisible by $2$.

It is divisible, thus, divide $1406$ by ${\color{green}2}$: $\frac{1406}{2} = {\color{red}703}$.

Determine whether $703$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $703$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $703$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $703$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $703$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $703$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $703$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $703$ is divisible by $19$.

It is divisible, thus, divide $703$ by ${\color{green}19}$: $\frac{703}{19} = {\color{red}37}$.

The prime number ${\color{green}37}$ has no other factors then $1$ and ${\color{green}37}$: $\frac{37}{37} = {\color{red}1}$.

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: $2812 = 2^{2} \cdot 19 \cdot 37$.

The prime factorization is $2812 = 2^{2} \cdot 19 \cdot 37$A.