# Prime factorization of $1233$

The calculator will find the prime factorization of $1233$, with steps shown.

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Find the prime factorization of $1233$.

### Solution

Start with the number $2$.

Determine whether $1233$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1233$ is divisible by $3$.

It is divisible, thus, divide $1233$ by ${\color{green}3}$: $\frac{1233}{3} = {\color{red}411}$.

Determine whether $411$ is divisible by $3$.

It is divisible, thus, divide $411$ by ${\color{green}3}$: $\frac{411}{3} = {\color{red}137}$.

The prime number ${\color{green}137}$ has no other factors then $1$ and ${\color{green}137}$: $\frac{137}{137} = {\color{red}1}$.

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: $1233 = 3^{2} \cdot 137$.

The prime factorization is $1233 = 3^{2} \cdot 137$A.