# Prime factorization of $824$

The calculator will find the prime factorization of $824$, with steps shown.

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Find the prime factorization of $824$.

### Solution

Start with the number $2$.

Determine whether $824$ is divisible by $2$.

It is divisible, thus, divide $824$ by ${\color{green}2}$: $\frac{824}{2} = {\color{red}412}$.

Determine whether $412$ is divisible by $2$.

It is divisible, thus, divide $412$ by ${\color{green}2}$: $\frac{412}{2} = {\color{red}206}$.

Determine whether $206$ is divisible by $2$.

It is divisible, thus, divide $206$ by ${\color{green}2}$: $\frac{206}{2} = {\color{red}103}$.

The prime number ${\color{green}103}$ has no other factors then $1$ and ${\color{green}103}$: $\frac{103}{103} = {\color{red}1}$.

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: $824 = 2^{3} \cdot 103$.

The prime factorization is $824 = 2^{3} \cdot 103$A.