Prime factorization of $$$3652$$$

Find the prime factorization of $$$3652$$$.

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

Determine whether $$$3652$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3652$$$ by $$${\color{green}2}$$$: $$$\frac{3652}{2} = {\color{red}1826}$$$.

Determine whether $$$1826$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1826$$$ by $$${\color{green}2}$$$: $$$\frac{1826}{2} = {\color{red}913}$$$.

Determine whether $$$913$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$913$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$913$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$913$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$913$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$913$$$ by $$${\color{green}11}$$$: $$$\frac{913}{11} = {\color{red}83}$$$.

The prime number $$${\color{green}83}$$$ has no other factors then $$$1$$$ and $$${\color{green}83}$$$: $$$\frac{83}{83} = {\color{red}1}$$$.

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: $$$3652 = 2^{2} \cdot 11 \cdot 83$$$.

The prime factorization is $$$3652 = 2^{2} \cdot 11 \cdot 83$$$A.