Prime factorization of $$$4074$$$

Find the prime factorization of $$$4074$$$.

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

Determine whether $$$4074$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4074$$$ by $$${\color{green}2}$$$: $$$\frac{4074}{2} = {\color{red}2037}$$$.

Determine whether $$$2037$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2037$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2037$$$ by $$${\color{green}3}$$$: $$$\frac{2037}{3} = {\color{red}679}$$$.

Determine whether $$$679$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$679$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$679$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$679$$$ by $$${\color{green}7}$$$: $$$\frac{679}{7} = {\color{red}97}$$$.

The prime number $$${\color{green}97}$$$ has no other factors then $$$1$$$ and $$${\color{green}97}$$$: $$$\frac{97}{97} = {\color{red}1}$$$.

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: $$$4074 = 2 \cdot 3 \cdot 7 \cdot 97$$$.

The prime factorization is $$$4074 = 2 \cdot 3 \cdot 7 \cdot 97$$$A.