Prime factorization of $$$1677$$$

Find the prime factorization of $$$1677$$$.

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

Determine whether $$$1677$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1677$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1677$$$ by $$${\color{green}3}$$$: $$$\frac{1677}{3} = {\color{red}559}$$$.

Determine whether $$$559$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$559$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$559$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$559$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$559$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$559$$$ by $$${\color{green}13}$$$: $$$\frac{559}{13} = {\color{red}43}$$$.

The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.

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: $$$1677 = 3 \cdot 13 \cdot 43$$$.

The prime factorization is $$$1677 = 3 \cdot 13 \cdot 43$$$A.