# Prime factorization of $1837$

The calculator will find the prime factorization of $1837$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $1837$.

### Solution

Start with the number $2$.

Determine whether $1837$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1837$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1837$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1837$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $1837$ is divisible by $11$.

It is divisible, thus, divide $1837$ by ${\color{green}11}$: $\frac{1837}{11} = {\color{red}167}$.

The prime number ${\color{green}167}$ has no other factors then $1$ and ${\color{green}167}$: $\frac{167}{167} = {\color{red}1}$.

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: $1837 = 11 \cdot 167$.

The prime factorization is $1837 = 11 \cdot 167$A.