Prime factorization of $$$885$$$

Find the prime factorization of $$$885$$$.

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

Determine whether $$$885$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$885$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$885$$$ by $$${\color{green}3}$$$: $$$\frac{885}{3} = {\color{red}295}$$$.

Determine whether $$$295$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$295$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$295$$$ by $$${\color{green}5}$$$: $$$\frac{295}{5} = {\color{red}59}$$$.

The prime number $$${\color{green}59}$$$ has no other factors then $$$1$$$ and $$${\color{green}59}$$$: $$$\frac{59}{59} = {\color{red}1}$$$.

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: $$$885 = 3 \cdot 5 \cdot 59$$$.

The prime factorization is $$$885 = 3 \cdot 5 \cdot 59$$$A.