Prime factorization of $$$1096$$$

Find the prime factorization of $$$1096$$$.

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

Determine whether $$$1096$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1096$$$ by $$${\color{green}2}$$$: $$$\frac{1096}{2} = {\color{red}548}$$$.

Determine whether $$$548$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$548$$$ by $$${\color{green}2}$$$: $$$\frac{548}{2} = {\color{red}274}$$$.

Determine whether $$$274$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$274$$$ by $$${\color{green}2}$$$: $$$\frac{274}{2} = {\color{red}137}$$$.

The prime number $$${\color{green}137}$$$ has no other factors then $$$1$$$ and $$${\color{green}137}$$$: $$$\frac{137}{137} = {\color{red}1}$$$.

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: $$$1096 = 2^{3} \cdot 137$$$.

The prime factorization is $$$1096 = 2^{3} \cdot 137$$$A.