Prime factorization of $$$3123$$$

Find the prime factorization of $$$3123$$$.

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

Determine whether $$$3123$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3123$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3123$$$ by $$${\color{green}3}$$$: $$$\frac{3123}{3} = {\color{red}1041}$$$.

Determine whether $$$1041$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1041$$$ by $$${\color{green}3}$$$: $$$\frac{1041}{3} = {\color{red}347}$$$.

The prime number $$${\color{green}347}$$$ has no other factors then $$$1$$$ and $$${\color{green}347}$$$: $$$\frac{347}{347} = {\color{red}1}$$$.

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: $$$3123 = 3^{2} \cdot 347$$$.

The prime factorization is $$$3123 = 3^{2} \cdot 347$$$A.