# Prime factorization of $2853$

The calculator will find the prime factorization of $2853$, with steps shown.

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Find the prime factorization of $2853$.

### Solution

Start with the number $2$.

Determine whether $2853$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2853$ is divisible by $3$.

It is divisible, thus, divide $2853$ by ${\color{green}3}$: $\frac{2853}{3} = {\color{red}951}$.

Determine whether $951$ is divisible by $3$.

It is divisible, thus, divide $951$ by ${\color{green}3}$: $\frac{951}{3} = {\color{red}317}$.

The prime number ${\color{green}317}$ has no other factors then $1$ and ${\color{green}317}$: $\frac{317}{317} = {\color{red}1}$.

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: $2853 = 3^{2} \cdot 317$.

The prime factorization is $2853 = 3^{2} \cdot 317$A.