Prime factorization of $$$1890$$$

Find the prime factorization of $$$1890$$$.

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

Determine whether $$$1890$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1890$$$ by $$${\color{green}2}$$$: $$$\frac{1890}{2} = {\color{red}945}$$$.

Determine whether $$$945$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$945$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$945$$$ by $$${\color{green}3}$$$: $$$\frac{945}{3} = {\color{red}315}$$$.

Determine whether $$$315$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$315$$$ by $$${\color{green}3}$$$: $$$\frac{315}{3} = {\color{red}105}$$$.

Determine whether $$$105$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$105$$$ by $$${\color{green}3}$$$: $$$\frac{105}{3} = {\color{red}35}$$$.

Determine whether $$$35$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$35$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$35$$$ by $$${\color{green}5}$$$: $$$\frac{35}{5} = {\color{red}7}$$$.

The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.

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: $$$1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7$$$.

The prime factorization is $$$1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7$$$A.