Prime factorization of $$$1975$$$

Find the prime factorization of $$$1975$$$.

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

Determine whether $$$1975$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1975$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1975$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1975$$$ by $$${\color{green}5}$$$: $$$\frac{1975}{5} = {\color{red}395}$$$.

Determine whether $$$395$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$395$$$ by $$${\color{green}5}$$$: $$$\frac{395}{5} = {\color{red}79}$$$.

The prime number $$${\color{green}79}$$$ has no other factors then $$$1$$$ and $$${\color{green}79}$$$: $$$\frac{79}{79} = {\color{red}1}$$$.

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: $$$1975 = 5^{2} \cdot 79$$$.

The prime factorization is $$$1975 = 5^{2} \cdot 79$$$A.