# Prime factorization of $1744$

The calculator will find the prime factorization of $1744$, with steps shown.

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Find the prime factorization of $1744$.

### Solution

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.