Prime factorization of $$$3692$$$

Find the prime factorization of $$$3692$$$.

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

Determine whether $$$3692$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3692$$$ by $$${\color{green}2}$$$: $$$\frac{3692}{2} = {\color{red}1846}$$$.

Determine whether $$$1846$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1846$$$ by $$${\color{green}2}$$$: $$$\frac{1846}{2} = {\color{red}923}$$$.

Determine whether $$$923$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$923$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$923$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$923$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$923$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$923$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$923$$$ by $$${\color{green}13}$$$: $$$\frac{923}{13} = {\color{red}71}$$$.

The prime number $$${\color{green}71}$$$ has no other factors then $$$1$$$ and $$${\color{green}71}$$$: $$$\frac{71}{71} = {\color{red}1}$$$.

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: $$$3692 = 2^{2} \cdot 13 \cdot 71$$$.

The prime factorization is $$$3692 = 2^{2} \cdot 13 \cdot 71$$$A.