Prime factorization of $$$224$$$

Find the prime factorization of $$$224$$$.

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

Determine whether $$$224$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$224$$$ by $$${\color{green}2}$$$: $$$\frac{224}{2} = {\color{red}112}$$$.

Determine whether $$$112$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$112$$$ by $$${\color{green}2}$$$: $$$\frac{112}{2} = {\color{red}56}$$$.

Determine whether $$$56$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$56$$$ by $$${\color{green}2}$$$: $$$\frac{56}{2} = {\color{red}28}$$$.

Determine whether $$$28$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$28$$$ by $$${\color{green}2}$$$: $$$\frac{28}{2} = {\color{red}14}$$$.

Determine whether $$$14$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$14$$$ by $$${\color{green}2}$$$: $$$\frac{14}{2} = {\color{red}7}$$$.

The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.

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: $$$224 = 2^{5} \cdot 7$$$.

The prime factorization is $$$224 = 2^{5} \cdot 7$$$A.