Prime factorization of $$$1758$$$

Find the prime factorization of $$$1758$$$.

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

Determine whether $$$1758$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1758$$$ by $$${\color{green}2}$$$: $$$\frac{1758}{2} = {\color{red}879}$$$.

Determine whether $$$879$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$879$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$879$$$ by $$${\color{green}3}$$$: $$$\frac{879}{3} = {\color{red}293}$$$.

The prime number $$${\color{green}293}$$$ has no other factors then $$$1$$$ and $$${\color{green}293}$$$: $$$\frac{293}{293} = {\color{red}1}$$$.

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: $$$1758 = 2 \cdot 3 \cdot 293$$$.

The prime factorization is $$$1758 = 2 \cdot 3 \cdot 293$$$A.