# Prime factorization of $2484$

The calculator will find the prime factorization of $2484$, with steps shown.

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Find the prime factorization of $2484$.

### Solution

Start with the number $2$.

Determine whether $2484$ is divisible by $2$.

It is divisible, thus, divide $2484$ by ${\color{green}2}$: $\frac{2484}{2} = {\color{red}1242}$.

Determine whether $1242$ is divisible by $2$.

It is divisible, thus, divide $1242$ by ${\color{green}2}$: $\frac{1242}{2} = {\color{red}621}$.

Determine whether $621$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $621$ is divisible by $3$.

It is divisible, thus, divide $621$ by ${\color{green}3}$: $\frac{621}{3} = {\color{red}207}$.

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: $2484 = 2^{2} \cdot 3^{3} \cdot 23$.

The prime factorization is $2484 = 2^{2} \cdot 3^{3} \cdot 23$A.