Prime factorization of $$$2527$$$

Find the prime factorization of $$$2527$$$.

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

Determine whether $$$2527$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2527$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2527$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2527$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$2527$$$ by $$${\color{green}7}$$$: $$$\frac{2527}{7} = {\color{red}361}$$$.

Determine whether $$$361$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$361$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$361$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$361$$$ is divisible by $$$17$$$.

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

The next prime number is $$$19$$$.

Determine whether $$$361$$$ is divisible by $$$19$$$.

It is divisible, thus, divide $$$361$$$ by $$${\color{green}19}$$$: $$$\frac{361}{19} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$2527 = 7 \cdot 19^{2}$$$.

The prime factorization is $$$2527 = 7 \cdot 19^{2}$$$A.