Prime factorization of $$$3176$$$

Find the prime factorization of $$$3176$$$.

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

Determine whether $$$3176$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3176$$$ by $$${\color{green}2}$$$: $$$\frac{3176}{2} = {\color{red}1588}$$$.

Determine whether $$$1588$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1588$$$ by $$${\color{green}2}$$$: $$$\frac{1588}{2} = {\color{red}794}$$$.

Determine whether $$$794$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$794$$$ by $$${\color{green}2}$$$: $$$\frac{794}{2} = {\color{red}397}$$$.

The prime number $$${\color{green}397}$$$ has no other factors then $$$1$$$ and $$${\color{green}397}$$$: $$$\frac{397}{397} = {\color{red}1}$$$.

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: $$$3176 = 2^{3} \cdot 397$$$.

The prime factorization is $$$3176 = 2^{3} \cdot 397$$$A.