Prime factorization of $$$4293$$$

Find the prime factorization of $$$4293$$$.

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

Determine whether $$$4293$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4293$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4293$$$ by $$${\color{green}3}$$$: $$$\frac{4293}{3} = {\color{red}1431}$$$.

Determine whether $$$1431$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1431$$$ by $$${\color{green}3}$$$: $$$\frac{1431}{3} = {\color{red}477}$$$.

Determine whether $$$477$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$477$$$ by $$${\color{green}3}$$$: $$$\frac{477}{3} = {\color{red}159}$$$.

Determine whether $$$159$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$159$$$ by $$${\color{green}3}$$$: $$$\frac{159}{3} = {\color{red}53}$$$.

The prime number $$${\color{green}53}$$$ has no other factors then $$$1$$$ and $$${\color{green}53}$$$: $$$\frac{53}{53} = {\color{red}1}$$$.

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: $$$4293 = 3^{4} \cdot 53$$$.

The prime factorization is $$$4293 = 3^{4} \cdot 53$$$A.