# Prime factorization of $2574$

The calculator will find the prime factorization of $2574$, with steps shown.

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Find the prime factorization of $2574$.

### Solution

Start with the number $2$.

Determine whether $2574$ is divisible by $2$.

It is divisible, thus, divide $2574$ by ${\color{green}2}$: $\frac{2574}{2} = {\color{red}1287}$.

Determine whether $1287$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1287$ is divisible by $3$.

It is divisible, thus, divide $1287$ by ${\color{green}3}$: $\frac{1287}{3} = {\color{red}429}$.

Determine whether $429$ is divisible by $3$.

It is divisible, thus, divide $429$ by ${\color{green}3}$: $\frac{429}{3} = {\color{red}143}$.

Determine whether $143$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $143$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $143$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $143$ is divisible by $11$.

It is divisible, thus, divide $143$ by ${\color{green}11}$: $\frac{143}{11} = {\color{red}13}$.

The prime number ${\color{green}13}$ has no other factors then $1$ and ${\color{green}13}$: $\frac{13}{13} = {\color{red}1}$.

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: $2574 = 2 \cdot 3^{2} \cdot 11 \cdot 13$.

The prime factorization is $2574 = 2 \cdot 3^{2} \cdot 11 \cdot 13$A.