# Prime factorization of $2583$

The calculator will find the prime factorization of $2583$, with steps shown.

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Find the prime factorization of $2583$.

### Solution

Start with the number $2$.

Determine whether $2583$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2583$ is divisible by $3$.

It is divisible, thus, divide $2583$ by ${\color{green}3}$: $\frac{2583}{3} = {\color{red}861}$.

Determine whether $861$ is divisible by $3$.

It is divisible, thus, divide $861$ by ${\color{green}3}$: $\frac{861}{3} = {\color{red}287}$.

Determine whether $287$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $287$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $287$ is divisible by $7$.

It is divisible, thus, divide $287$ by ${\color{green}7}$: $\frac{287}{7} = {\color{red}41}$.

The prime number ${\color{green}41}$ has no other factors then $1$ and ${\color{green}41}$: $\frac{41}{41} = {\color{red}1}$.

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: $2583 = 3^{2} \cdot 7 \cdot 41$.

The prime factorization is $2583 = 3^{2} \cdot 7 \cdot 41$A.