Prime factorization of $$$3670$$$

Find the prime factorization of $$$3670$$$.

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

Determine whether $$$3670$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3670$$$ by $$${\color{green}2}$$$: $$$\frac{3670}{2} = {\color{red}1835}$$$.

Determine whether $$$1835$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1835$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1835$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1835$$$ by $$${\color{green}5}$$$: $$$\frac{1835}{5} = {\color{red}367}$$$.

The prime number $$${\color{green}367}$$$ has no other factors then $$$1$$$ and $$${\color{green}367}$$$: $$$\frac{367}{367} = {\color{red}1}$$$.

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: $$$3670 = 2 \cdot 5 \cdot 367$$$.

The prime factorization is $$$3670 = 2 \cdot 5 \cdot 367$$$A.