# Prime factorization of $3692$

The calculator will find the prime factorization of $3692$, with steps shown.

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Find the prime factorization of $3692$.

### Solution

Start with the number $2$.

Determine whether $3692$ is divisible by $2$.

It is divisible, thus, divide $3692$ by ${\color{green}2}$: $\frac{3692}{2} = {\color{red}1846}$.

Determine whether $1846$ is divisible by $2$.

It is divisible, thus, divide $1846$ by ${\color{green}2}$: $\frac{1846}{2} = {\color{red}923}$.

Determine whether $923$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $923$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $923$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $923$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $923$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $923$ is divisible by $13$.

It is divisible, thus, divide $923$ by ${\color{green}13}$: $\frac{923}{13} = {\color{red}71}$.

The prime number ${\color{green}71}$ has no other factors then $1$ and ${\color{green}71}$: $\frac{71}{71} = {\color{red}1}$.

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: $3692 = 2^{2} \cdot 13 \cdot 71$.

The prime factorization is $3692 = 2^{2} \cdot 13 \cdot 71$A.