Prime factorization of $$$474$$$

Find the prime factorization of $$$474$$$.

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

Determine whether $$$474$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$474$$$ by $$${\color{green}2}$$$: $$$\frac{474}{2} = {\color{red}237}$$$.

Determine whether $$$237$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$237$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$237$$$ by $$${\color{green}3}$$$: $$$\frac{237}{3} = {\color{red}79}$$$.

The prime number $$${\color{green}79}$$$ has no other factors then $$$1$$$ and $$${\color{green}79}$$$: $$$\frac{79}{79} = {\color{red}1}$$$.

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: $$$474 = 2 \cdot 3 \cdot 79$$$.

The prime factorization is $$$474 = 2 \cdot 3 \cdot 79$$$A.