# Prime factorization of $2684$

The calculator will find the prime factorization of $2684$, with steps shown.

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Find the prime factorization of $2684$.

### Solution

Start with the number $2$.

Determine whether $2684$ is divisible by $2$.

It is divisible, thus, divide $2684$ by ${\color{green}2}$: $\frac{2684}{2} = {\color{red}1342}$.

Determine whether $1342$ is divisible by $2$.

It is divisible, thus, divide $1342$ by ${\color{green}2}$: $\frac{1342}{2} = {\color{red}671}$.

Determine whether $671$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $671$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $671$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $671$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $671$ is divisible by $11$.

It is divisible, thus, divide $671$ by ${\color{green}11}$: $\frac{671}{11} = {\color{red}61}$.

The prime number ${\color{green}61}$ has no other factors then $1$ and ${\color{green}61}$: $\frac{61}{61} = {\color{red}1}$.

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: $2684 = 2^{2} \cdot 11 \cdot 61$.

The prime factorization is $2684 = 2^{2} \cdot 11 \cdot 61$A.