Prime factorization of $$$1850$$$

Find the prime factorization of $$$1850$$$.

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.