Prime factorization of $$$3530$$$

Find the prime factorization of $$$3530$$$.

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

Determine whether $$$3530$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3530$$$ by $$${\color{green}2}$$$: $$$\frac{3530}{2} = {\color{red}1765}$$$.

Determine whether $$$1765$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1765$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1765$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1765$$$ by $$${\color{green}5}$$$: $$$\frac{1765}{5} = {\color{red}353}$$$.

The prime number $$${\color{green}353}$$$ has no other factors then $$$1$$$ and $$${\color{green}353}$$$: $$$\frac{353}{353} = {\color{red}1}$$$.

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: $$$3530 = 2 \cdot 5 \cdot 353$$$.

The prime factorization is $$$3530 = 2 \cdot 5 \cdot 353$$$A.