Prime factorization of $$$464$$$

Find the prime factorization of $$$464$$$.

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.