Prime factorization of $$$3732$$$

Find the prime factorization of $$$3732$$$.

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

Determine whether $$$3732$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3732$$$ by $$${\color{green}2}$$$: $$$\frac{3732}{2} = {\color{red}1866}$$$.

Determine whether $$$1866$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1866$$$ by $$${\color{green}2}$$$: $$$\frac{1866}{2} = {\color{red}933}$$$.

Determine whether $$$933$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$933$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$933$$$ by $$${\color{green}3}$$$: $$$\frac{933}{3} = {\color{red}311}$$$.

The prime number $$${\color{green}311}$$$ has no other factors then $$$1$$$ and $$${\color{green}311}$$$: $$$\frac{311}{311} = {\color{red}1}$$$.

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: $$$3732 = 2^{2} \cdot 3 \cdot 311$$$.

The prime factorization is $$$3732 = 2^{2} \cdot 3 \cdot 311$$$A.