# Prime factorization of $2178$

The calculator will find the prime factorization of $2178$, with steps shown.

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Find the prime factorization of $2178$.

### Solution

Start with the number $2$.

Determine whether $2178$ is divisible by $2$.

It is divisible, thus, divide $2178$ by ${\color{green}2}$: $\frac{2178}{2} = {\color{red}1089}$.

Determine whether $1089$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1089$ is divisible by $3$.

It is divisible, thus, divide $1089$ by ${\color{green}3}$: $\frac{1089}{3} = {\color{red}363}$.

Determine whether $363$ is divisible by $3$.

It is divisible, thus, divide $363$ by ${\color{green}3}$: $\frac{363}{3} = {\color{red}121}$.

Determine whether $121$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $121$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $121$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $121$ is divisible by $11$.

It is divisible, thus, divide $121$ by ${\color{green}11}$: $\frac{121}{11} = {\color{red}11}$.

The prime number ${\color{green}11}$ has no other factors then $1$ and ${\color{green}11}$: $\frac{11}{11} = {\color{red}1}$.

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: $2178 = 2 \cdot 3^{2} \cdot 11^{2}$.

The prime factorization is $2178 = 2 \cdot 3^{2} \cdot 11^{2}$A.