# Prime factorization of $4632$

The calculator will find the prime factorization of $4632$, with steps shown.

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Find the prime factorization of $4632$.

### Solution

Start with the number $2$.

Determine whether $4632$ is divisible by $2$.

It is divisible, thus, divide $4632$ by ${\color{green}2}$: $\frac{4632}{2} = {\color{red}2316}$.

Determine whether $2316$ is divisible by $2$.

It is divisible, thus, divide $2316$ by ${\color{green}2}$: $\frac{2316}{2} = {\color{red}1158}$.

Determine whether $1158$ is divisible by $2$.

It is divisible, thus, divide $1158$ by ${\color{green}2}$: $\frac{1158}{2} = {\color{red}579}$.

Determine whether $579$ is divisible by $2$.

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

The next prime number is $3$.

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: $4632 = 2^{3} \cdot 3 \cdot 193$.

The prime factorization is $4632 = 2^{3} \cdot 3 \cdot 193$A.