Prime factorization of $$$3040$$$

Find the prime factorization of $$$3040$$$.

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

Determine whether $$$3040$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3040$$$ by $$${\color{green}2}$$$: $$$\frac{3040}{2} = {\color{red}1520}$$$.

Determine whether $$$1520$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1520$$$ by $$${\color{green}2}$$$: $$$\frac{1520}{2} = {\color{red}760}$$$.

Determine whether $$$760$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$760$$$ by $$${\color{green}2}$$$: $$$\frac{760}{2} = {\color{red}380}$$$.

Determine whether $$$380$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$380$$$ by $$${\color{green}2}$$$: $$$\frac{380}{2} = {\color{red}190}$$$.

Determine whether $$$190$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$190$$$ by $$${\color{green}2}$$$: $$$\frac{190}{2} = {\color{red}95}$$$.

Determine whether $$$95$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$95$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$95$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$95$$$ by $$${\color{green}5}$$$: $$$\frac{95}{5} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$3040 = 2^{5} \cdot 5 \cdot 19$$$.

The prime factorization is $$$3040 = 2^{5} \cdot 5 \cdot 19$$$A.