# Prime factorization of $855$

The calculator will find the prime factorization of $855$, with steps shown.

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Find the prime factorization of $855$.

### Solution

Start with the number $2$.

Determine whether $855$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $855$ is divisible by $3$.

It is divisible, thus, divide $855$ by ${\color{green}3}$: $\frac{855}{3} = {\color{red}285}$.

Determine whether $285$ is divisible by $3$.

It is divisible, thus, divide $285$ by ${\color{green}3}$: $\frac{285}{3} = {\color{red}95}$.

Determine whether $95$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $95$ is divisible by $5$.

It is divisible, thus, divide $95$ by ${\color{green}5}$: $\frac{95}{5} = {\color{red}19}$.

The prime number ${\color{green}19}$ has no other factors then $1$ and ${\color{green}19}$: $\frac{19}{19} = {\color{red}1}$.

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: $855 = 3^{2} \cdot 5 \cdot 19$.

The prime factorization is $855 = 3^{2} \cdot 5 \cdot 19$A.