Prime factorization of $$$708$$$

Find the prime factorization of $$$708$$$.

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

Determine whether $$$708$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$708$$$ by $$${\color{green}2}$$$: $$$\frac{708}{2} = {\color{red}354}$$$.

Determine whether $$$354$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$354$$$ by $$${\color{green}2}$$$: $$$\frac{354}{2} = {\color{red}177}$$$.

Determine whether $$$177$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$177$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$177$$$ by $$${\color{green}3}$$$: $$$\frac{177}{3} = {\color{red}59}$$$.

The prime number $$${\color{green}59}$$$ has no other factors then $$$1$$$ and $$${\color{green}59}$$$: $$$\frac{59}{59} = {\color{red}1}$$$.

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: $$$708 = 2^{2} \cdot 3 \cdot 59$$$.

The prime factorization is $$$708 = 2^{2} \cdot 3 \cdot 59$$$A.