# Prime factorization of $2124$

The calculator will find the prime factorization of $2124$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $2124$.

### Solution

Start with the number $2$.

Determine whether $2124$ is divisible by $2$.

It is divisible, thus, divide $2124$ by ${\color{green}2}$: $\frac{2124}{2} = {\color{red}1062}$.

Determine whether $1062$ is divisible by $2$.

It is divisible, thus, divide $1062$ by ${\color{green}2}$: $\frac{1062}{2} = {\color{red}531}$.

Determine whether $531$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $531$ is divisible by $3$.

It is divisible, thus, divide $531$ by ${\color{green}3}$: $\frac{531}{3} = {\color{red}177}$.

Determine whether $177$ is divisible by $3$.

It is divisible, thus, divide $177$ by ${\color{green}3}$: $\frac{177}{3} = {\color{red}59}$.

The prime number ${\color{green}59}$ has no other factors then $1$ and ${\color{green}59}$: $\frac{59}{59} = {\color{red}1}$.

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: $2124 = 2^{2} \cdot 3^{2} \cdot 59$.

The prime factorization is $2124 = 2^{2} \cdot 3^{2} \cdot 59$A.