# Prime factorization of $1854$

The calculator will find the prime factorization of $1854$, with steps shown.

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Find the prime factorization of $1854$.

### Solution

Start with the number $2$.

Determine whether $1854$ is divisible by $2$.

It is divisible, thus, divide $1854$ by ${\color{green}2}$: $\frac{1854}{2} = {\color{red}927}$.

Determine whether $927$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $927$ is divisible by $3$.

It is divisible, thus, divide $927$ by ${\color{green}3}$: $\frac{927}{3} = {\color{red}309}$.

Determine whether $309$ is divisible by $3$.

It is divisible, thus, divide $309$ by ${\color{green}3}$: $\frac{309}{3} = {\color{red}103}$.

The prime number ${\color{green}103}$ has no other factors then $1$ and ${\color{green}103}$: $\frac{103}{103} = {\color{red}1}$.

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: $1854 = 2 \cdot 3^{2} \cdot 103$.

The prime factorization is $1854 = 2 \cdot 3^{2} \cdot 103$A.