# Prime factorization of $3553$

The calculator will find the prime factorization of $3553$, 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 $3553$.

### Solution

Start with the number $2$.

Determine whether $3553$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3553$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $3553$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $3553$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $3553$ is divisible by $11$.

It is divisible, thus, divide $3553$ by ${\color{green}11}$: $\frac{3553}{11} = {\color{red}323}$.

Determine whether $323$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $323$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $323$ is divisible by $17$.

It is divisible, thus, divide $323$ by ${\color{green}17}$: $\frac{323}{17} = {\color{red}19}$.

The prime number ${\color{green}19}$ has no other factors then $1$ and ${\color{green}19}$: $\frac{19}{19} = {\color{red}1}$.

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: $3553 = 11 \cdot 17 \cdot 19$.

The prime factorization is $3553 = 11 \cdot 17 \cdot 19$A.