Prime factorization of $2820$

Find the prime factorization of $2820$.

Start with the number $2$.

Determine whether $2820$ is divisible by $2$.

It is divisible, thus, divide $2820$ by ${\color{green}2}$: $\frac{2820}{2} = {\color{red}1410}$.

Determine whether $1410$ is divisible by $2$.

It is divisible, thus, divide $1410$ by ${\color{green}2}$: $\frac{1410}{2} = {\color{red}705}$.

Determine whether $705$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $705$ is divisible by $3$.

It is divisible, thus, divide $705$ by ${\color{green}3}$: $\frac{705}{3} = {\color{red}235}$.

Determine whether $235$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $235$ is divisible by $5$.

It is divisible, thus, divide $235$ by ${\color{green}5}$: $\frac{235}{5} = {\color{red}47}$.

The prime number ${\color{green}47}$ has no other factors then $1$ and ${\color{green}47}$: $\frac{47}{47} = {\color{red}1}$.

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: $2820 = 2^{2} \cdot 3 \cdot 5 \cdot 47$.

The prime factorization is $2820 = 2^{2} \cdot 3 \cdot 5 \cdot 47$A.