Prime factorization of $$$3515$$$

Find the prime factorization of $$$3515$$$.

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

Determine whether $$$3515$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3515$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$3515$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$3515$$$ by $$${\color{green}5}$$$: $$$\frac{3515}{5} = {\color{red}703}$$$.

Determine whether $$$703$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$703$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$703$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$703$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$703$$$ is divisible by $$$17$$$.

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

The next prime number is $$$19$$$.

Determine whether $$$703$$$ is divisible by $$$19$$$.

It is divisible, thus, divide $$$703$$$ by $$${\color{green}19}$$$: $$$\frac{703}{19} = {\color{red}37}$$$.

The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.

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: $$$3515 = 5 \cdot 19 \cdot 37$$$.

The prime factorization is $$$3515 = 5 \cdot 19 \cdot 37$$$A.