Prime factorization of $$$3521$$$

Find the prime factorization of $$$3521$$$.

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

Determine whether $$$3521$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3521$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$3521$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$3521$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$3521$$$ by $$${\color{green}7}$$$: $$$\frac{3521}{7} = {\color{red}503}$$$.

The prime number $$${\color{green}503}$$$ has no other factors then $$$1$$$ and $$${\color{green}503}$$$: $$$\frac{503}{503} = {\color{red}1}$$$.

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: $$$3521 = 7 \cdot 503$$$.

The prime factorization is $$$3521 = 7 \cdot 503$$$A.