Prime factorization of $$$1380$$$

Find the prime factorization of $$$1380$$$.

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

Determine whether $$$1380$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1380$$$ by $$${\color{green}2}$$$: $$$\frac{1380}{2} = {\color{red}690}$$$.

Determine whether $$$690$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$690$$$ by $$${\color{green}2}$$$: $$$\frac{690}{2} = {\color{red}345}$$$.

Determine whether $$$345$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$345$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$345$$$ by $$${\color{green}3}$$$: $$$\frac{345}{3} = {\color{red}115}$$$.

Determine whether $$$115$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$115$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$115$$$ by $$${\color{green}5}$$$: $$$\frac{115}{5} = {\color{red}23}$$$.

The prime number $$${\color{green}23}$$$ has no other factors then $$$1$$$ and $$${\color{green}23}$$$: $$$\frac{23}{23} = {\color{red}1}$$$.

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: $$$1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23$$$.

The prime factorization is $$$1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23$$$A.