# Prime factorization of $3546$

The calculator will find the prime factorization of $3546$, with steps shown.

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Find the prime factorization of $3546$.

### Solution

Start with the number $2$.

Determine whether $3546$ is divisible by $2$.

It is divisible, thus, divide $3546$ by ${\color{green}2}$: $\frac{3546}{2} = {\color{red}1773}$.

Determine whether $1773$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1773$ is divisible by $3$.

It is divisible, thus, divide $1773$ by ${\color{green}3}$: $\frac{1773}{3} = {\color{red}591}$.

Determine whether $591$ is divisible by $3$.

It is divisible, thus, divide $591$ by ${\color{green}3}$: $\frac{591}{3} = {\color{red}197}$.

The prime number ${\color{green}197}$ has no other factors then $1$ and ${\color{green}197}$: $\frac{197}{197} = {\color{red}1}$.

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: $3546 = 2 \cdot 3^{2} \cdot 197$.

The prime factorization is $3546 = 2 \cdot 3^{2} \cdot 197$A.