Prime factorization of $$$2072$$$

Find the prime factorization of $$$2072$$$.

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

Determine whether $$$2072$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2072$$$ by $$${\color{green}2}$$$: $$$\frac{2072}{2} = {\color{red}1036}$$$.

Determine whether $$$1036$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1036$$$ by $$${\color{green}2}$$$: $$$\frac{1036}{2} = {\color{red}518}$$$.

Determine whether $$$518$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$518$$$ by $$${\color{green}2}$$$: $$$\frac{518}{2} = {\color{red}259}$$$.

Determine whether $$$259$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$259$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$259$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$259$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$259$$$ by $$${\color{green}7}$$$: $$$\frac{259}{7} = {\color{red}37}$$$.

The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.

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: $$$2072 = 2^{3} \cdot 7 \cdot 37$$$.

The prime factorization is $$$2072 = 2^{3} \cdot 7 \cdot 37$$$A.