Prime factorization of $$$1771$$$

Find the prime factorization of $$$1771$$$.

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

Determine whether $$$1771$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1771$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1771$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1771$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$1771$$$ by $$${\color{green}7}$$$: $$$\frac{1771}{7} = {\color{red}253}$$$.

Determine whether $$$253$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$253$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$253$$$ by $$${\color{green}11}$$$: $$$\frac{253}{11} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

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: $$$1771 = 7 \cdot 11 \cdot 23$$$.

The prime factorization is $$$1771 = 7 \cdot 11 \cdot 23$$$A.