# Prime factorization of $1578$

The calculator will find the prime factorization of $1578$, with steps shown.

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Find the prime factorization of $1578$.

### Solution

Start with the number $2$.

Determine whether $1578$ is divisible by $2$.

It is divisible, thus, divide $1578$ by ${\color{green}2}$: $\frac{1578}{2} = {\color{red}789}$.

Determine whether $789$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $789$ is divisible by $3$.

It is divisible, thus, divide $789$ by ${\color{green}3}$: $\frac{789}{3} = {\color{red}263}$.

The prime number ${\color{green}263}$ has no other factors then $1$ and ${\color{green}263}$: $\frac{263}{263} = {\color{red}1}$.

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: $1578 = 2 \cdot 3 \cdot 263$.

The prime factorization is $1578 = 2 \cdot 3 \cdot 263$A.