Prime factorization of $$$3355$$$

Find the prime factorization of $$$3355$$$.

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

Determine whether $$$3355$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3355$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$3355$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$3355$$$ by $$${\color{green}5}$$$: $$$\frac{3355}{5} = {\color{red}671}$$$.

Determine whether $$$671$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$671$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$671$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$671$$$ by $$${\color{green}11}$$$: $$$\frac{671}{11} = {\color{red}61}$$$.

The prime number $$${\color{green}61}$$$ has no other factors then $$$1$$$ and $$${\color{green}61}$$$: $$$\frac{61}{61} = {\color{red}1}$$$.

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: $$$3355 = 5 \cdot 11 \cdot 61$$$.

The prime factorization is $$$3355 = 5 \cdot 11 \cdot 61$$$A.