Prime factorization of $$$669$$$

Find the prime factorization of $$$669$$$.

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

Determine whether $$$669$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$669$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$669$$$ by $$${\color{green}3}$$$: $$$\frac{669}{3} = {\color{red}223}$$$.

The prime number $$${\color{green}223}$$$ has no other factors then $$$1$$$ and $$${\color{green}223}$$$: $$$\frac{223}{223} = {\color{red}1}$$$.

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: $$$669 = 3 \cdot 223$$$.

The prime factorization is $$$669 = 3 \cdot 223$$$A.