# Prime factorization of $310$

The calculator will find the prime factorization of $310$, with steps shown.

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Find the prime factorization of $310$.

### Solution

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.