Prime factorization of $$$1562$$$

Find the prime factorization of $$$1562$$$.

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

Determine whether $$$1562$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1562$$$ by $$${\color{green}2}$$$: $$$\frac{1562}{2} = {\color{red}781}$$$.

Determine whether $$$781$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$781$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$781$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$781$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$781$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$781$$$ by $$${\color{green}11}$$$: $$$\frac{781}{11} = {\color{red}71}$$$.

The prime number $$${\color{green}71}$$$ has no other factors then $$$1$$$ and $$${\color{green}71}$$$: $$$\frac{71}{71} = {\color{red}1}$$$.

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: $$$1562 = 2 \cdot 11 \cdot 71$$$.

The prime factorization is $$$1562 = 2 \cdot 11 \cdot 71$$$A.