Prime factorization of $$$2944$$$

Find the prime factorization of $$$2944$$$.

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.