Prime factorization of $$$3772$$$

Find the prime factorization of $$$3772$$$.

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

Determine whether $$$3772$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3772$$$ by $$${\color{green}2}$$$: $$$\frac{3772}{2} = {\color{red}1886}$$$.

Determine whether $$$1886$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1886$$$ by $$${\color{green}2}$$$: $$$\frac{1886}{2} = {\color{red}943}$$$.

Determine whether $$$943$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$943$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$943$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$943$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$943$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$943$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$943$$$ is divisible by $$$17$$$.

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

The next prime number is $$$19$$$.

Determine whether $$$943$$$ is divisible by $$$19$$$.

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

The next prime number is $$$23$$$.

Determine whether $$$943$$$ is divisible by $$$23$$$.

It is divisible, thus, divide $$$943$$$ by $$${\color{green}23}$$$: $$$\frac{943}{23} = {\color{red}41}$$$.

The prime number $$${\color{green}41}$$$ has no other factors then $$$1$$$ and $$${\color{green}41}$$$: $$$\frac{41}{41} = {\color{red}1}$$$.

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: $$$3772 = 2^{2} \cdot 23 \cdot 41$$$.

The prime factorization is $$$3772 = 2^{2} \cdot 23 \cdot 41$$$A.