Prime factorization of $$$786$$$

Find the prime factorization of $$$786$$$.

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

Determine whether $$$786$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$786$$$ by $$${\color{green}2}$$$: $$$\frac{786}{2} = {\color{red}393}$$$.

Determine whether $$$393$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$393$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$393$$$ by $$${\color{green}3}$$$: $$$\frac{393}{3} = {\color{red}131}$$$.

The prime number $$${\color{green}131}$$$ has no other factors then $$$1$$$ and $$${\color{green}131}$$$: $$$\frac{131}{131} = {\color{red}1}$$$.

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: $$$786 = 2 \cdot 3 \cdot 131$$$.

The prime factorization is $$$786 = 2 \cdot 3 \cdot 131$$$A.