Prime factorization of $$$3870$$$

Find the prime factorization of $$$3870$$$.

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

Determine whether $$$3870$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3870$$$ by $$${\color{green}2}$$$: $$$\frac{3870}{2} = {\color{red}1935}$$$.

Determine whether $$$1935$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1935$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1935$$$ by $$${\color{green}3}$$$: $$$\frac{1935}{3} = {\color{red}645}$$$.

Determine whether $$$645$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$645$$$ by $$${\color{green}3}$$$: $$$\frac{645}{3} = {\color{red}215}$$$.

Determine whether $$$215$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$215$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$215$$$ by $$${\color{green}5}$$$: $$$\frac{215}{5} = {\color{red}43}$$$.

The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.

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: $$$3870 = 2 \cdot 3^{2} \cdot 5 \cdot 43$$$.

The prime factorization is $$$3870 = 2 \cdot 3^{2} \cdot 5 \cdot 43$$$A.