Prime factorization of $$$3771$$$

Find the prime factorization of $$$3771$$$.

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

Determine whether $$$3771$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3771$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3771$$$ by $$${\color{green}3}$$$: $$$\frac{3771}{3} = {\color{red}1257}$$$.

Determine whether $$$1257$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1257$$$ by $$${\color{green}3}$$$: $$$\frac{1257}{3} = {\color{red}419}$$$.

The prime number $$${\color{green}419}$$$ has no other factors then $$$1$$$ and $$${\color{green}419}$$$: $$$\frac{419}{419} = {\color{red}1}$$$.

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: $$$3771 = 3^{2} \cdot 419$$$.

The prime factorization is $$$3771 = 3^{2} \cdot 419$$$A.