# Prime factorization of $1850$

The calculator will find the prime factorization of $1850$, with steps shown.

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Find the prime factorization of $1850$.

### Solution

Start with the number $2$.

Determine whether $1850$ is divisible by $2$.

It is divisible, thus, divide $1850$ by ${\color{green}2}$: $\frac{1850}{2} = {\color{red}925}$.

Determine whether $925$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $925$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $925$ is divisible by $5$.

It is divisible, thus, divide $925$ by ${\color{green}5}$: $\frac{925}{5} = {\color{red}185}$.

Determine whether $185$ is divisible by $5$.

It is divisible, thus, divide $185$ by ${\color{green}5}$: $\frac{185}{5} = {\color{red}37}$.

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: $1850 = 2 \cdot 5^{2} \cdot 37$.

The prime factorization is $1850 = 2 \cdot 5^{2} \cdot 37$A.