# Prime factorization of $3798$

The calculator will find the prime factorization of $3798$, with steps shown.

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Find the prime factorization of $3798$.

### Solution

Start with the number $2$.

Determine whether $3798$ is divisible by $2$.

It is divisible, thus, divide $3798$ by ${\color{green}2}$: $\frac{3798}{2} = {\color{red}1899}$.

Determine whether $1899$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1899$ is divisible by $3$.

It is divisible, thus, divide $1899$ by ${\color{green}3}$: $\frac{1899}{3} = {\color{red}633}$.

Determine whether $633$ is divisible by $3$.

It is divisible, thus, divide $633$ by ${\color{green}3}$: $\frac{633}{3} = {\color{red}211}$.

The prime number ${\color{green}211}$ has no other factors then $1$ and ${\color{green}211}$: $\frac{211}{211} = {\color{red}1}$.

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: $3798 = 2 \cdot 3^{2} \cdot 211$.

The prime factorization is $3798 = 2 \cdot 3^{2} \cdot 211$A.