# Prime factorization of $464$

The calculator will find the prime factorization of $464$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $464$.

### Solution

Start with the number $2$.

Determine whether $464$ is divisible by $2$.

It is divisible, thus, divide $464$ by ${\color{green}2}$: $\frac{464}{2} = {\color{red}232}$.

Determine whether $232$ is divisible by $2$.

It is divisible, thus, divide $232$ by ${\color{green}2}$: $\frac{232}{2} = {\color{red}116}$.

Determine whether $116$ is divisible by $2$.

It is divisible, thus, divide $116$ by ${\color{green}2}$: $\frac{116}{2} = {\color{red}58}$.

Determine whether $58$ is divisible by $2$.

It is divisible, thus, divide $58$ by ${\color{green}2}$: $\frac{58}{2} = {\color{red}29}$.

The prime number ${\color{green}29}$ has no other factors then $1$ and ${\color{green}29}$: $\frac{29}{29} = {\color{red}1}$.

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: $464 = 2^{4} \cdot 29$.

The prime factorization is $464 = 2^{4} \cdot 29$A.