Prime factorization of $$$868$$$

Find the prime factorization of $$$868$$$.

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

Determine whether $$$868$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$868$$$ by $$${\color{green}2}$$$: $$$\frac{868}{2} = {\color{red}434}$$$.

Determine whether $$$434$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$434$$$ by $$${\color{green}2}$$$: $$$\frac{434}{2} = {\color{red}217}$$$.

Determine whether $$$217$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$217$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$217$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$217$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$217$$$ by $$${\color{green}7}$$$: $$$\frac{217}{7} = {\color{red}31}$$$.

The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.

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: $$$868 = 2^{2} \cdot 7 \cdot 31$$$.

The prime factorization is $$$868 = 2^{2} \cdot 7 \cdot 31$$$A.