# Prime factorization of $4494$

The calculator will find the prime factorization of $4494$, 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 $4494$.

### Solution

Start with the number $2$.

Determine whether $4494$ is divisible by $2$.

It is divisible, thus, divide $4494$ by ${\color{green}2}$: $\frac{4494}{2} = {\color{red}2247}$.

Determine whether $2247$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2247$ is divisible by $3$.

It is divisible, thus, divide $2247$ by ${\color{green}3}$: $\frac{2247}{3} = {\color{red}749}$.

Determine whether $749$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $749$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $749$ is divisible by $7$.

It is divisible, thus, divide $749$ by ${\color{green}7}$: $\frac{749}{7} = {\color{red}107}$.

The prime number ${\color{green}107}$ has no other factors then $1$ and ${\color{green}107}$: $\frac{107}{107} = {\color{red}1}$.

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: $4494 = 2 \cdot 3 \cdot 7 \cdot 107$.

The prime factorization is $4494 = 2 \cdot 3 \cdot 7 \cdot 107$A.