# Prime factorization of $3690$

The calculator will find the prime factorization of $3690$, with steps shown.

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Find the prime factorization of $3690$.

### Solution

Start with the number $2$.

Determine whether $3690$ is divisible by $2$.

It is divisible, thus, divide $3690$ by ${\color{green}2}$: $\frac{3690}{2} = {\color{red}1845}$.

Determine whether $1845$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1845$ is divisible by $3$.

It is divisible, thus, divide $1845$ by ${\color{green}3}$: $\frac{1845}{3} = {\color{red}615}$.

Determine whether $615$ is divisible by $3$.

It is divisible, thus, divide $615$ by ${\color{green}3}$: $\frac{615}{3} = {\color{red}205}$.

Determine whether $205$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $205$ is divisible by $5$.

It is divisible, thus, divide $205$ by ${\color{green}5}$: $\frac{205}{5} = {\color{red}41}$.

The prime number ${\color{green}41}$ has no other factors then $1$ and ${\color{green}41}$: $\frac{41}{41} = {\color{red}1}$.

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: $3690 = 2 \cdot 3^{2} \cdot 5 \cdot 41$.

The prime factorization is $3690 = 2 \cdot 3^{2} \cdot 5 \cdot 41$A.