# Prime factorization of $4558$

The calculator will find the prime factorization of $4558$, 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 $4558$.

### Solution

Start with the number $2$.

Determine whether $4558$ is divisible by $2$.

It is divisible, thus, divide $4558$ by ${\color{green}2}$: $\frac{4558}{2} = {\color{red}2279}$.

Determine whether $2279$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2279$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2279$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $2279$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $2279$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $2279$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $2279$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $2279$ is divisible by $19$.

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

The next prime number is $23$.

Determine whether $2279$ is divisible by $23$.

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

The next prime number is $29$.

Determine whether $2279$ is divisible by $29$.

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

The next prime number is $31$.

Determine whether $2279$ is divisible by $31$.

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

The next prime number is $37$.

Determine whether $2279$ is divisible by $37$.

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

The next prime number is $41$.

Determine whether $2279$ is divisible by $41$.

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

The next prime number is $43$.

Determine whether $2279$ is divisible by $43$.

It is divisible, thus, divide $2279$ by ${\color{green}43}$: $\frac{2279}{43} = {\color{red}53}$.

The prime number ${\color{green}53}$ has no other factors then $1$ and ${\color{green}53}$: $\frac{53}{53} = {\color{red}1}$.

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: $4558 = 2 \cdot 43 \cdot 53$.

The prime factorization is $4558 = 2 \cdot 43 \cdot 53$A.