# Prime factorization of $3474$

The calculator will find the prime factorization of $3474$, with steps shown.

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Find the prime factorization of $3474$.

### Solution

Start with the number $2$.

Determine whether $3474$ is divisible by $2$.

It is divisible, thus, divide $3474$ by ${\color{green}2}$: $\frac{3474}{2} = {\color{red}1737}$.

Determine whether $1737$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1737$ is divisible by $3$.

It is divisible, thus, divide $1737$ by ${\color{green}3}$: $\frac{1737}{3} = {\color{red}579}$.

Determine whether $579$ is divisible by $3$.

It is divisible, thus, divide $579$ by ${\color{green}3}$: $\frac{579}{3} = {\color{red}193}$.

The prime number ${\color{green}193}$ has no other factors then $1$ and ${\color{green}193}$: $\frac{193}{193} = {\color{red}1}$.

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: $3474 = 2 \cdot 3^{2} \cdot 193$.

The prime factorization is $3474 = 2 \cdot 3^{2} \cdot 193$A.