Prime factorization of $$$1744$$$

Find the prime factorization of $$$1744$$$.

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

Determine whether $$$1744$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1744$$$ by $$${\color{green}2}$$$: $$$\frac{1744}{2} = {\color{red}872}$$$.

Determine whether $$$872$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$872$$$ by $$${\color{green}2}$$$: $$$\frac{872}{2} = {\color{red}436}$$$.

Determine whether $$$436$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$436$$$ by $$${\color{green}2}$$$: $$$\frac{436}{2} = {\color{red}218}$$$.

Determine whether $$$218$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$218$$$ by $$${\color{green}2}$$$: $$$\frac{218}{2} = {\color{red}109}$$$.

The prime number $$${\color{green}109}$$$ has no other factors then $$$1$$$ and $$${\color{green}109}$$$: $$$\frac{109}{109} = {\color{red}1}$$$.

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: $$$1744 = 2^{4} \cdot 109$$$.

The prime factorization is $$$1744 = 2^{4} \cdot 109$$$A.