# Prime factorization of $3492$

The calculator will find the prime factorization of $3492$, with steps shown.

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Find the prime factorization of $3492$.

### Solution

Start with the number $2$.

Determine whether $3492$ is divisible by $2$.

It is divisible, thus, divide $3492$ by ${\color{green}2}$: $\frac{3492}{2} = {\color{red}1746}$.

Determine whether $1746$ is divisible by $2$.

It is divisible, thus, divide $1746$ by ${\color{green}2}$: $\frac{1746}{2} = {\color{red}873}$.

Determine whether $873$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $873$ is divisible by $3$.

It is divisible, thus, divide $873$ by ${\color{green}3}$: $\frac{873}{3} = {\color{red}291}$.

Determine whether $291$ is divisible by $3$.

It is divisible, thus, divide $291$ by ${\color{green}3}$: $\frac{291}{3} = {\color{red}97}$.

The prime number ${\color{green}97}$ has no other factors then $1$ and ${\color{green}97}$: $\frac{97}{97} = {\color{red}1}$.

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: $3492 = 2^{2} \cdot 3^{2} \cdot 97$.

The prime factorization is $3492 = 2^{2} \cdot 3^{2} \cdot 97$A.