# Prime factorization of $4692$

The calculator will find the prime factorization of $4692$, with steps shown.

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Find the prime factorization of $4692$.

### Solution

Start with the number $2$.

Determine whether $4692$ is divisible by $2$.

It is divisible, thus, divide $4692$ by ${\color{green}2}$: $\frac{4692}{2} = {\color{red}2346}$.

Determine whether $2346$ is divisible by $2$.

It is divisible, thus, divide $2346$ by ${\color{green}2}$: $\frac{2346}{2} = {\color{red}1173}$.

Determine whether $1173$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1173$ is divisible by $3$.

It is divisible, thus, divide $1173$ by ${\color{green}3}$: $\frac{1173}{3} = {\color{red}391}$.

Determine whether $391$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $391$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $391$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $391$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $391$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $391$ is divisible by $17$.

It is divisible, thus, divide $391$ by ${\color{green}17}$: $\frac{391}{17} = {\color{red}23}$.

The prime number ${\color{green}23}$ has no other factors then $1$ and ${\color{green}23}$: $\frac{23}{23} = {\color{red}1}$.

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: $4692 = 2^{2} \cdot 3 \cdot 17 \cdot 23$.

The prime factorization is $4692 = 2^{2} \cdot 3 \cdot 17 \cdot 23$A.