Prime factorization of $$$310$$$

Find the prime factorization of $$$310$$$.

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

Determine whether $$$310$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$310$$$ by $$${\color{green}2}$$$: $$$\frac{310}{2} = {\color{red}155}$$$.

Determine whether $$$155$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$155$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$155$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$155$$$ by $$${\color{green}5}$$$: $$$\frac{155}{5} = {\color{red}31}$$$.

The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.

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: $$$310 = 2 \cdot 5 \cdot 31$$$.

The prime factorization is $$$310 = 2 \cdot 5 \cdot 31$$$A.