Prime factorization of $$$1526$$$

Find the prime factorization of $$$1526$$$.

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

Determine whether $$$1526$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1526$$$ by $$${\color{green}2}$$$: $$$\frac{1526}{2} = {\color{red}763}$$$.

Determine whether $$$763$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$763$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$763$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$763$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$763$$$ by $$${\color{green}7}$$$: $$$\frac{763}{7} = {\color{red}109}$$$.

The prime number $$${\color{green}109}$$$ has no other factors then $$$1$$$ and $$${\color{green}109}$$$: $$$\frac{109}{109} = {\color{red}1}$$$.

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: $$$1526 = 2 \cdot 7 \cdot 109$$$.

The prime factorization is $$$1526 = 2 \cdot 7 \cdot 109$$$A.