Prime factorization of $$$4053$$$

Find the prime factorization of $$$4053$$$.

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

Determine whether $$$4053$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4053$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4053$$$ by $$${\color{green}3}$$$: $$$\frac{4053}{3} = {\color{red}1351}$$$.

Determine whether $$$1351$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1351$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1351$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$1351$$$ by $$${\color{green}7}$$$: $$$\frac{1351}{7} = {\color{red}193}$$$.

The prime number $$${\color{green}193}$$$ has no other factors then $$$1$$$ and $$${\color{green}193}$$$: $$$\frac{193}{193} = {\color{red}1}$$$.

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: $$$4053 = 3 \cdot 7 \cdot 193$$$.

The prime factorization is $$$4053 = 3 \cdot 7 \cdot 193$$$A.