Prime factorization of $$$1510$$$

Find the prime factorization of $$$1510$$$.

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

Determine whether $$$1510$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1510$$$ by $$${\color{green}2}$$$: $$$\frac{1510}{2} = {\color{red}755}$$$.

Determine whether $$$755$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$755$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$755$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$755$$$ by $$${\color{green}5}$$$: $$$\frac{755}{5} = {\color{red}151}$$$.

The prime number $$${\color{green}151}$$$ has no other factors then $$$1$$$ and $$${\color{green}151}$$$: $$$\frac{151}{151} = {\color{red}1}$$$.

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: $$$1510 = 2 \cdot 5 \cdot 151$$$.

The prime factorization is $$$1510 = 2 \cdot 5 \cdot 151$$$A.