Prime factorization of $$$2075$$$

Find the prime factorization of $$$2075$$$.

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

Determine whether $$$2075$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2075$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2075$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$2075$$$ by $$${\color{green}5}$$$: $$$\frac{2075}{5} = {\color{red}415}$$$.

Determine whether $$$415$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$415$$$ by $$${\color{green}5}$$$: $$$\frac{415}{5} = {\color{red}83}$$$.

The prime number $$${\color{green}83}$$$ has no other factors then $$$1$$$ and $$${\color{green}83}$$$: $$$\frac{83}{83} = {\color{red}1}$$$.

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: $$$2075 = 5^{2} \cdot 83$$$.

The prime factorization is $$$2075 = 5^{2} \cdot 83$$$A.