Prime factorization of $$$3115$$$

Find the prime factorization of $$$3115$$$.

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

Determine whether $$$3115$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3115$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$3115$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$3115$$$ by $$${\color{green}5}$$$: $$$\frac{3115}{5} = {\color{red}623}$$$.

Determine whether $$$623$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$623$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$623$$$ by $$${\color{green}7}$$$: $$$\frac{623}{7} = {\color{red}89}$$$.

The prime number $$${\color{green}89}$$$ has no other factors then $$$1$$$ and $$${\color{green}89}$$$: $$$\frac{89}{89} = {\color{red}1}$$$.

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: $$$3115 = 5 \cdot 7 \cdot 89$$$.

The prime factorization is $$$3115 = 5 \cdot 7 \cdot 89$$$A.