Prime factorization of $$$1854$$$

Find the prime factorization of $$$1854$$$.

Start with the number $$$2$$$.

Determine whether $$$1854$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1854$$$ by $$${\color{green}2}$$$: $$$\frac{1854}{2} = {\color{red}927}$$$.

Determine whether $$$927$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$927$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$927$$$ by $$${\color{green}3}$$$: $$$\frac{927}{3} = {\color{red}309}$$$.

Determine whether $$$309$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$309$$$ by $$${\color{green}3}$$$: $$$\frac{309}{3} = {\color{red}103}$$$.

The prime number $$${\color{green}103}$$$ has no other factors then $$$1$$$ and $$${\color{green}103}$$$: $$$\frac{103}{103} = {\color{red}1}$$$.

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: $$$1854 = 2 \cdot 3^{2} \cdot 103$$$.

The prime factorization is $$$1854 = 2 \cdot 3^{2} \cdot 103$$$A.