Prime factorization of $$$1675$$$

Find the prime factorization of $$$1675$$$.

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

Determine whether $$$1675$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1675$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1675$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1675$$$ by $$${\color{green}5}$$$: $$$\frac{1675}{5} = {\color{red}335}$$$.

Determine whether $$$335$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$335$$$ by $$${\color{green}5}$$$: $$$\frac{335}{5} = {\color{red}67}$$$.

The prime number $$${\color{green}67}$$$ has no other factors then $$$1$$$ and $$${\color{green}67}$$$: $$$\frac{67}{67} = {\color{red}1}$$$.

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: $$$1675 = 5^{2} \cdot 67$$$.

The prime factorization is $$$1675 = 5^{2} \cdot 67$$$A.