# Prime factorization of $2646$

The calculator will find the prime factorization of $2646$, with steps shown.

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Find the prime factorization of $2646$.

### Solution

Start with the number $2$.

Determine whether $2646$ is divisible by $2$.

It is divisible, thus, divide $2646$ by ${\color{green}2}$: $\frac{2646}{2} = {\color{red}1323}$.

Determine whether $1323$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1323$ is divisible by $3$.

It is divisible, thus, divide $1323$ by ${\color{green}3}$: $\frac{1323}{3} = {\color{red}441}$.

Determine whether $441$ is divisible by $3$.

It is divisible, thus, divide $441$ by ${\color{green}3}$: $\frac{441}{3} = {\color{red}147}$.

Determine whether $147$ is divisible by $3$.

It is divisible, thus, divide $147$ by ${\color{green}3}$: $\frac{147}{3} = {\color{red}49}$.

Determine whether $49$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $49$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $49$ is divisible by $7$.

It is divisible, thus, divide $49$ by ${\color{green}7}$: $\frac{49}{7} = {\color{red}7}$.

The prime number ${\color{green}7}$ has no other factors then $1$ and ${\color{green}7}$: $\frac{7}{7} = {\color{red}1}$.

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: $2646 = 2 \cdot 3^{3} \cdot 7^{2}$.

The prime factorization is $2646 = 2 \cdot 3^{3} \cdot 7^{2}$A.