Prime factorization of $$$3190$$$

Find the prime factorization of $$$3190$$$.

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

Determine whether $$$3190$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3190$$$ by $$${\color{green}2}$$$: $$$\frac{3190}{2} = {\color{red}1595}$$$.

Determine whether $$$1595$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1595$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1595$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1595$$$ by $$${\color{green}5}$$$: $$$\frac{1595}{5} = {\color{red}319}$$$.

Determine whether $$$319$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$319$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$319$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$319$$$ by $$${\color{green}11}$$$: $$$\frac{319}{11} = {\color{red}29}$$$.

The prime number $$${\color{green}29}$$$ has no other factors then $$$1$$$ and $$${\color{green}29}$$$: $$$\frac{29}{29} = {\color{red}1}$$$.

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: $$$3190 = 2 \cdot 5 \cdot 11 \cdot 29$$$.

The prime factorization is $$$3190 = 2 \cdot 5 \cdot 11 \cdot 29$$$A.