# Prime factorization of $1098$

The calculator will find the prime factorization of $1098$, with steps shown.

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Find the prime factorization of $1098$.

### Solution

Start with the number $2$.

Determine whether $1098$ is divisible by $2$.

It is divisible, thus, divide $1098$ by ${\color{green}2}$: $\frac{1098}{2} = {\color{red}549}$.

Determine whether $549$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $549$ is divisible by $3$.

It is divisible, thus, divide $549$ by ${\color{green}3}$: $\frac{549}{3} = {\color{red}183}$.

Determine whether $183$ is divisible by $3$.

It is divisible, thus, divide $183$ by ${\color{green}3}$: $\frac{183}{3} = {\color{red}61}$.

The prime number ${\color{green}61}$ has no other factors then $1$ and ${\color{green}61}$: $\frac{61}{61} = {\color{red}1}$.

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: $1098 = 2 \cdot 3^{2} \cdot 61$.

The prime factorization is $1098 = 2 \cdot 3^{2} \cdot 61$A.