# Prime factorization of $3584$

The calculator will find the prime factorization of $3584$, with steps shown.

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Find the prime factorization of $3584$.

### Solution

Start with the number $2$.

Determine whether $3584$ is divisible by $2$.

It is divisible, thus, divide $3584$ by ${\color{green}2}$: $\frac{3584}{2} = {\color{red}1792}$.

Determine whether $1792$ is divisible by $2$.

It is divisible, thus, divide $1792$ by ${\color{green}2}$: $\frac{1792}{2} = {\color{red}896}$.

Determine whether $896$ is divisible by $2$.

It is divisible, thus, divide $896$ by ${\color{green}2}$: $\frac{896}{2} = {\color{red}448}$.

Determine whether $448$ is divisible by $2$.

It is divisible, thus, divide $448$ by ${\color{green}2}$: $\frac{448}{2} = {\color{red}224}$.

Determine whether $224$ is divisible by $2$.

It is divisible, thus, divide $224$ by ${\color{green}2}$: $\frac{224}{2} = {\color{red}112}$.

Determine whether $112$ is divisible by $2$.

It is divisible, thus, divide $112$ by ${\color{green}2}$: $\frac{112}{2} = {\color{red}56}$.

Determine whether $56$ is divisible by $2$.

It is divisible, thus, divide $56$ by ${\color{green}2}$: $\frac{56}{2} = {\color{red}28}$.

Determine whether $28$ is divisible by $2$.

It is divisible, thus, divide $28$ by ${\color{green}2}$: $\frac{28}{2} = {\color{red}14}$.

Determine whether $14$ is divisible by $2$.

It is divisible, thus, divide $14$ by ${\color{green}2}$: $\frac{14}{2} = {\color{red}7}$.

The prime number ${\color{green}7}$ has no other factors then $1$ and ${\color{green}7}$: $\frac{7}{7} = {\color{red}1}$.

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: $3584 = 2^{9} \cdot 7$.

The prime factorization is $3584 = 2^{9} \cdot 7$A.