Prime factorization of $$$3535$$$

Find the prime factorization of $$$3535$$$.

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

Determine whether $$$3535$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3535$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$3535$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$3535$$$ by $$${\color{green}5}$$$: $$$\frac{3535}{5} = {\color{red}707}$$$.

Determine whether $$$707$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$707$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$707$$$ by $$${\color{green}7}$$$: $$$\frac{707}{7} = {\color{red}101}$$$.

The prime number $$${\color{green}101}$$$ has no other factors then $$$1$$$ and $$${\color{green}101}$$$: $$$\frac{101}{101} = {\color{red}1}$$$.

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: $$$3535 = 5 \cdot 7 \cdot 101$$$.

The prime factorization is $$$3535 = 5 \cdot 7 \cdot 101$$$A.