# Prime factorization of $1962$

The calculator will find the prime factorization of $1962$, with steps shown.

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Find the prime factorization of $1962$.

### Solution

Start with the number $2$.

Determine whether $1962$ is divisible by $2$.

It is divisible, thus, divide $1962$ by ${\color{green}2}$: $\frac{1962}{2} = {\color{red}981}$.

Determine whether $981$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $981$ is divisible by $3$.

It is divisible, thus, divide $981$ by ${\color{green}3}$: $\frac{981}{3} = {\color{red}327}$.

Determine whether $327$ is divisible by $3$.

It is divisible, thus, divide $327$ by ${\color{green}3}$: $\frac{327}{3} = {\color{red}109}$.

The prime number ${\color{green}109}$ has no other factors then $1$ and ${\color{green}109}$: $\frac{109}{109} = {\color{red}1}$.

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: $1962 = 2 \cdot 3^{2} \cdot 109$.

The prime factorization is $1962 = 2 \cdot 3^{2} \cdot 109$A.