Prime factorization of $$$2940$$$

Find the prime factorization of $$$2940$$$.

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

Determine whether $$$2940$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2940$$$ by $$${\color{green}2}$$$: $$$\frac{2940}{2} = {\color{red}1470}$$$.

Determine whether $$$1470$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1470$$$ by $$${\color{green}2}$$$: $$$\frac{1470}{2} = {\color{red}735}$$$.

Determine whether $$$735$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$735$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$735$$$ by $$${\color{green}3}$$$: $$$\frac{735}{3} = {\color{red}245}$$$.

Determine whether $$$245$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$245$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$245$$$ by $$${\color{green}5}$$$: $$$\frac{245}{5} = {\color{red}49}$$$.

Determine whether $$$49$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$49$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$49$$$ by $$${\color{green}7}$$$: $$$\frac{49}{7} = {\color{red}7}$$$.

The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.

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: $$$2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2}$$$.

The prime factorization is $$$2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2}$$$A.