# Prime factorization of $4232$

The calculator will find the prime factorization of $4232$, with steps shown.

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Find the prime factorization of $4232$.

### Solution

Start with the number $2$.

Determine whether $4232$ is divisible by $2$.

It is divisible, thus, divide $4232$ by ${\color{green}2}$: $\frac{4232}{2} = {\color{red}2116}$.

Determine whether $2116$ is divisible by $2$.

It is divisible, thus, divide $2116$ by ${\color{green}2}$: $\frac{2116}{2} = {\color{red}1058}$.

Determine whether $1058$ is divisible by $2$.

It is divisible, thus, divide $1058$ by ${\color{green}2}$: $\frac{1058}{2} = {\color{red}529}$.

Determine whether $529$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $529$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $529$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $529$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $529$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $529$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $529$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $529$ is divisible by $19$.

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

The next prime number is $23$.

Determine whether $529$ is divisible by $23$.

It is divisible, thus, divide $529$ by ${\color{green}23}$: $\frac{529}{23} = {\color{red}23}$.

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: $4232 = 2^{3} \cdot 23^{2}$.

The prime factorization is $4232 = 2^{3} \cdot 23^{2}$A.