Prime factorization of $$$1782$$$

Find the prime factorization of $$$1782$$$.

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

Determine whether $$$1782$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1782$$$ by $$${\color{green}2}$$$: $$$\frac{1782}{2} = {\color{red}891}$$$.

Determine whether $$$891$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$891$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$891$$$ by $$${\color{green}3}$$$: $$$\frac{891}{3} = {\color{red}297}$$$.

Determine whether $$$297$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$297$$$ by $$${\color{green}3}$$$: $$$\frac{297}{3} = {\color{red}99}$$$.

Determine whether $$$99$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$99$$$ by $$${\color{green}3}$$$: $$$\frac{99}{3} = {\color{red}33}$$$.

Determine whether $$$33$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$33$$$ by $$${\color{green}3}$$$: $$$\frac{33}{3} = {\color{red}11}$$$.

The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.

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: $$$1782 = 2 \cdot 3^{4} \cdot 11$$$.

The prime factorization is $$$1782 = 2 \cdot 3^{4} \cdot 11$$$A.