Prime factorization of $$$2465$$$

Find the prime factorization of $$$2465$$$.

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

Determine whether $$$2465$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2465$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2465$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$2465$$$ by $$${\color{green}5}$$$: $$$\frac{2465}{5} = {\color{red}493}$$$.

Determine whether $$$493$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$493$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$493$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$493$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$493$$$ is divisible by $$$17$$$.

It is divisible, thus, divide $$$493$$$ by $$${\color{green}17}$$$: $$$\frac{493}{17} = {\color{red}29}$$$.

The prime number $$${\color{green}29}$$$ has no other factors then $$$1$$$ and $$${\color{green}29}$$$: $$$\frac{29}{29} = {\color{red}1}$$$.

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: $$$2465 = 5 \cdot 17 \cdot 29$$$.

The prime factorization is $$$2465 = 5 \cdot 17 \cdot 29$$$A.