# Prime factorization of $2944$

The calculator will find the prime factorization of $2944$, with steps shown.

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Find the prime factorization of $2944$.

### Solution

Start with the number $2$.

Determine whether $2944$ is divisible by $2$.

It is divisible, thus, divide $2944$ by ${\color{green}2}$: $\frac{2944}{2} = {\color{red}1472}$.

Determine whether $1472$ is divisible by $2$.

It is divisible, thus, divide $1472$ by ${\color{green}2}$: $\frac{1472}{2} = {\color{red}736}$.

Determine whether $736$ is divisible by $2$.

It is divisible, thus, divide $736$ by ${\color{green}2}$: $\frac{736}{2} = {\color{red}368}$.

Determine whether $368$ is divisible by $2$.

It is divisible, thus, divide $368$ by ${\color{green}2}$: $\frac{368}{2} = {\color{red}184}$.

Determine whether $184$ is divisible by $2$.

It is divisible, thus, divide $184$ by ${\color{green}2}$: $\frac{184}{2} = {\color{red}92}$.

Determine whether $92$ is divisible by $2$.

It is divisible, thus, divide $92$ by ${\color{green}2}$: $\frac{92}{2} = {\color{red}46}$.

Determine whether $46$ is divisible by $2$.

It is divisible, thus, divide $46$ by ${\color{green}2}$: $\frac{46}{2} = {\color{red}23}$.

The prime number ${\color{green}23}$ has no other factors then $1$ and ${\color{green}23}$: $\frac{23}{23} = {\color{red}1}$.

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: $2944 = 2^{7} \cdot 23$.

The prime factorization is $2944 = 2^{7} \cdot 23$A.