# Prime factorization of $486$

The calculator will find the prime factorization of $486$, with steps shown.

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Find the prime factorization of $486$.

### Solution

Start with the number $2$.

Determine whether $486$ is divisible by $2$.

It is divisible, thus, divide $486$ by ${\color{green}2}$: $\frac{486}{2} = {\color{red}243}$.

Determine whether $243$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $243$ is divisible by $3$.

It is divisible, thus, divide $243$ by ${\color{green}3}$: $\frac{243}{3} = {\color{red}81}$.

Determine whether $81$ is divisible by $3$.

It is divisible, thus, divide $81$ by ${\color{green}3}$: $\frac{81}{3} = {\color{red}27}$.

Determine whether $27$ is divisible by $3$.

It is divisible, thus, divide $27$ by ${\color{green}3}$: $\frac{27}{3} = {\color{red}9}$.

Determine whether $9$ is divisible by $3$.

It is divisible, thus, divide $9$ by ${\color{green}3}$: $\frac{9}{3} = {\color{red}3}$.

The prime number ${\color{green}3}$ has no other factors then $1$ and ${\color{green}3}$: $\frac{3}{3} = {\color{red}1}$.

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: $486 = 2 \cdot 3^{5}$.

The prime factorization is $486 = 2 \cdot 3^{5}$A.