# Prime factorization of $1254$

The calculator will find the prime factorization of $1254$, with steps shown.

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Find the prime factorization of $1254$.

### Solution

Start with the number $2$.

Determine whether $1254$ is divisible by $2$.

It is divisible, thus, divide $1254$ by ${\color{green}2}$: $\frac{1254}{2} = {\color{red}627}$.

Determine whether $627$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $627$ is divisible by $3$.

It is divisible, thus, divide $627$ by ${\color{green}3}$: $\frac{627}{3} = {\color{red}209}$.

Determine whether $209$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $209$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $209$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $209$ is divisible by $11$.

It is divisible, thus, divide $209$ by ${\color{green}11}$: $\frac{209}{11} = {\color{red}19}$.

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: $1254 = 2 \cdot 3 \cdot 11 \cdot 19$.

The prime factorization is $1254 = 2 \cdot 3 \cdot 11 \cdot 19$A.