Prime factorization of $$$3474$$$

Find the prime factorization of $$$3474$$$.

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

Determine whether $$$3474$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3474$$$ by $$${\color{green}2}$$$: $$$\frac{3474}{2} = {\color{red}1737}$$$.

Determine whether $$$1737$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1737$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1737$$$ by $$${\color{green}3}$$$: $$$\frac{1737}{3} = {\color{red}579}$$$.

Determine whether $$$579$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$579$$$ by $$${\color{green}3}$$$: $$$\frac{579}{3} = {\color{red}193}$$$.

The prime number $$${\color{green}193}$$$ has no other factors then $$$1$$$ and $$${\color{green}193}$$$: $$$\frac{193}{193} = {\color{red}1}$$$.

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: $$$3474 = 2 \cdot 3^{2} \cdot 193$$$.

The prime factorization is $$$3474 = 2 \cdot 3^{2} \cdot 193$$$A.