Prime factorization of $$$1448$$$

Find the prime factorization of $$$1448$$$.

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

Determine whether $$$1448$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1448$$$ by $$${\color{green}2}$$$: $$$\frac{1448}{2} = {\color{red}724}$$$.

Determine whether $$$724$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$724$$$ by $$${\color{green}2}$$$: $$$\frac{724}{2} = {\color{red}362}$$$.

Determine whether $$$362$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$362$$$ by $$${\color{green}2}$$$: $$$\frac{362}{2} = {\color{red}181}$$$.

The prime number $$${\color{green}181}$$$ has no other factors then $$$1$$$ and $$${\color{green}181}$$$: $$$\frac{181}{181} = {\color{red}1}$$$.

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: $$$1448 = 2^{3} \cdot 181$$$.

The prime factorization is $$$1448 = 2^{3} \cdot 181$$$A.