Prime factorization of $$$3480$$$

Find the prime factorization of $$$3480$$$.

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

Determine whether $$$3480$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3480$$$ by $$${\color{green}2}$$$: $$$\frac{3480}{2} = {\color{red}1740}$$$.

Determine whether $$$1740$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1740$$$ by $$${\color{green}2}$$$: $$$\frac{1740}{2} = {\color{red}870}$$$.

Determine whether $$$870$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$870$$$ by $$${\color{green}2}$$$: $$$\frac{870}{2} = {\color{red}435}$$$.

Determine whether $$$435$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$435$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$435$$$ by $$${\color{green}3}$$$: $$$\frac{435}{3} = {\color{red}145}$$$.

Determine whether $$$145$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$145$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$145$$$ by $$${\color{green}5}$$$: $$$\frac{145}{5} = {\color{red}29}$$$.

The prime number $$${\color{green}29}$$$ has no other factors then $$$1$$$ and $$${\color{green}29}$$$: $$$\frac{29}{29} = {\color{red}1}$$$.

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: $$$3480 = 2^{3} \cdot 3 \cdot 5 \cdot 29$$$.

The prime factorization is $$$3480 = 2^{3} \cdot 3 \cdot 5 \cdot 29$$$A.