# Prime factorization of $3810$

The calculator will find the prime factorization of $3810$, with steps shown.

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Find the prime factorization of $3810$.

### Solution

Start with the number $2$.

Determine whether $3810$ is divisible by $2$.

It is divisible, thus, divide $3810$ by ${\color{green}2}$: $\frac{3810}{2} = {\color{red}1905}$.

Determine whether $1905$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1905$ is divisible by $3$.

It is divisible, thus, divide $1905$ by ${\color{green}3}$: $\frac{1905}{3} = {\color{red}635}$.

Determine whether $635$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $635$ is divisible by $5$.

It is divisible, thus, divide $635$ by ${\color{green}5}$: $\frac{635}{5} = {\color{red}127}$.

The prime number ${\color{green}127}$ has no other factors then $1$ and ${\color{green}127}$: $\frac{127}{127} = {\color{red}1}$.

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: $3810 = 2 \cdot 3 \cdot 5 \cdot 127$.

The prime factorization is $3810 = 2 \cdot 3 \cdot 5 \cdot 127$A.