Prime factorization of $$$3885$$$

Find the prime factorization of $$$3885$$$.

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

Determine whether $$$3885$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3885$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3885$$$ by $$${\color{green}3}$$$: $$$\frac{3885}{3} = {\color{red}1295}$$$.

Determine whether $$$1295$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1295$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1295$$$ by $$${\color{green}5}$$$: $$$\frac{1295}{5} = {\color{red}259}$$$.

Determine whether $$$259$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$259$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$259$$$ by $$${\color{green}7}$$$: $$$\frac{259}{7} = {\color{red}37}$$$.

The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.

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: $$$3885 = 3 \cdot 5 \cdot 7 \cdot 37$$$.

The prime factorization is $$$3885 = 3 \cdot 5 \cdot 7 \cdot 37$$$A.