Prime factorization of $$$3075$$$

Find the prime factorization of $$$3075$$$.

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

Determine whether $$$3075$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3075$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3075$$$ by $$${\color{green}3}$$$: $$$\frac{3075}{3} = {\color{red}1025}$$$.

Determine whether $$$1025$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1025$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1025$$$ by $$${\color{green}5}$$$: $$$\frac{1025}{5} = {\color{red}205}$$$.

Determine whether $$$205$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$205$$$ by $$${\color{green}5}$$$: $$$\frac{205}{5} = {\color{red}41}$$$.

The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.

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: $$$3075 = 3 \cdot 5^{2} \cdot 41$$$.

The prime factorization is $$$3075 = 3 \cdot 5^{2} \cdot 41$$$A.