Prime factorization of $$$3465$$$

Find the prime factorization of $$$3465$$$.

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

Determine whether $$$3465$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3465$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3465$$$ by $$${\color{green}3}$$$: $$$\frac{3465}{3} = {\color{red}1155}$$$.

Determine whether $$$1155$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1155$$$ by $$${\color{green}3}$$$: $$$\frac{1155}{3} = {\color{red}385}$$$.

Determine whether $$$385$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$385$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$385$$$ by $$${\color{green}5}$$$: $$$\frac{385}{5} = {\color{red}77}$$$.

Determine whether $$$77$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$77$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$77$$$ by $$${\color{green}7}$$$: $$$\frac{77}{7} = {\color{red}11}$$$.

The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.

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: $$$3465 = 3^{2} \cdot 5 \cdot 7 \cdot 11$$$.

The prime factorization is $$$3465 = 3^{2} \cdot 5 \cdot 7 \cdot 11$$$A.