# Prime factorization of $1024$

The calculator will find the prime factorization of $1024$, with steps shown.

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Find the prime factorization of $1024$.

### Solution

Start with the number $2$.

Determine whether $1024$ is divisible by $2$.

It is divisible, thus, divide $1024$ by ${\color{green}2}$: $\frac{1024}{2} = {\color{red}512}$.

Determine whether $512$ is divisible by $2$.

It is divisible, thus, divide $512$ by ${\color{green}2}$: $\frac{512}{2} = {\color{red}256}$.

Determine whether $256$ is divisible by $2$.

It is divisible, thus, divide $256$ by ${\color{green}2}$: $\frac{256}{2} = {\color{red}128}$.

Determine whether $128$ is divisible by $2$.

It is divisible, thus, divide $128$ by ${\color{green}2}$: $\frac{128}{2} = {\color{red}64}$.

Determine whether $64$ is divisible by $2$.

It is divisible, thus, divide $64$ by ${\color{green}2}$: $\frac{64}{2} = {\color{red}32}$.

Determine whether $32$ is divisible by $2$.

It is divisible, thus, divide $32$ by ${\color{green}2}$: $\frac{32}{2} = {\color{red}16}$.

Determine whether $16$ is divisible by $2$.

It is divisible, thus, divide $16$ by ${\color{green}2}$: $\frac{16}{2} = {\color{red}8}$.

Determine whether $8$ is divisible by $2$.

It is divisible, thus, divide $8$ by ${\color{green}2}$: $\frac{8}{2} = {\color{red}4}$.

Determine whether $4$ is divisible by $2$.

It is divisible, thus, divide $4$ by ${\color{green}2}$: $\frac{4}{2} = {\color{red}2}$.

The prime number ${\color{green}2}$ has no other factors then $1$ and ${\color{green}2}$: $\frac{2}{2} = {\color{red}1}$.

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: $1024 = 2^{10}$.

The prime factorization is $1024 = 2^{10}$A.