# Prime factorization of $828$

The calculator will find the prime factorization of $828$, with steps shown.

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Find the prime factorization of $828$.

### Solution

Start with the number $2$.

Determine whether $828$ is divisible by $2$.

It is divisible, thus, divide $828$ by ${\color{green}2}$: $\frac{828}{2} = {\color{red}414}$.

Determine whether $414$ is divisible by $2$.

It is divisible, thus, divide $414$ by ${\color{green}2}$: $\frac{414}{2} = {\color{red}207}$.

Determine whether $207$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $207$ is divisible by $3$.

It is divisible, thus, divide $207$ by ${\color{green}3}$: $\frac{207}{3} = {\color{red}69}$.

Determine whether $69$ is divisible by $3$.

It is divisible, thus, divide $69$ by ${\color{green}3}$: $\frac{69}{3} = {\color{red}23}$.

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: $828 = 2^{2} \cdot 3^{2} \cdot 23$.

The prime factorization is $828 = 2^{2} \cdot 3^{2} \cdot 23$A.