Prime factorization of $$$1631$$$

Find the prime factorization of $$$1631$$$.

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

Determine whether $$$1631$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1631$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1631$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1631$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$1631$$$ by $$${\color{green}7}$$$: $$$\frac{1631}{7} = {\color{red}233}$$$.

The prime number $$${\color{green}233}$$$ has no other factors then $$$1$$$ and $$${\color{green}233}$$$: $$$\frac{233}{233} = {\color{red}1}$$$.

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: $$$1631 = 7 \cdot 233$$$.

The prime factorization is $$$1631 = 7 \cdot 233$$$A.