Prime factorization of $$$1680$$$

Find the prime factorization of $$$1680$$$.

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

Determine whether $$$1680$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1680$$$ by $$${\color{green}2}$$$: $$$\frac{1680}{2} = {\color{red}840}$$$.

Determine whether $$$840$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$840$$$ by $$${\color{green}2}$$$: $$$\frac{840}{2} = {\color{red}420}$$$.

Determine whether $$$420$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$420$$$ by $$${\color{green}2}$$$: $$$\frac{420}{2} = {\color{red}210}$$$.

Determine whether $$$210$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$210$$$ by $$${\color{green}2}$$$: $$$\frac{210}{2} = {\color{red}105}$$$.

Determine whether $$$105$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$105$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$105$$$ by $$${\color{green}3}$$$: $$$\frac{105}{3} = {\color{red}35}$$$.

Determine whether $$$35$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$35$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$35$$$ by $$${\color{green}5}$$$: $$$\frac{35}{5} = {\color{red}7}$$$.

The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.

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: $$$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$$$.

The prime factorization is $$$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$$$A.