Prime factorization of $$$1464$$$

Find the prime factorization of $$$1464$$$.

Start with the number $$$2$$$.

Determine whether $$$1464$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1464$$$ by $$${\color{green}2}$$$: $$$\frac{1464}{2} = {\color{red}732}$$$.

Determine whether $$$732$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$732$$$ by $$${\color{green}2}$$$: $$$\frac{732}{2} = {\color{red}366}$$$.

Determine whether $$$366$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$366$$$ by $$${\color{green}2}$$$: $$$\frac{366}{2} = {\color{red}183}$$$.

Determine whether $$$183$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$183$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$183$$$ by $$${\color{green}3}$$$: $$$\frac{183}{3} = {\color{red}61}$$$.

The prime number $$${\color{green}61}$$$ has no other factors then $$$1$$$ and $$${\color{green}61}$$$: $$$\frac{61}{61} = {\color{red}1}$$$.

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: $$$1464 = 2^{3} \cdot 3 \cdot 61$$$.

The prime factorization is $$$1464 = 2^{3} \cdot 3 \cdot 61$$$A.