# Prime factorization of $2114$

The calculator will find the prime factorization of $2114$, with steps shown.

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Find the prime factorization of $2114$.

### Solution

Start with the number $2$.

Determine whether $2114$ is divisible by $2$.

It is divisible, thus, divide $2114$ by ${\color{green}2}$: $\frac{2114}{2} = {\color{red}1057}$.

Determine whether $1057$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1057$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1057$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1057$ is divisible by $7$.

It is divisible, thus, divide $1057$ by ${\color{green}7}$: $\frac{1057}{7} = {\color{red}151}$.

The prime number ${\color{green}151}$ has no other factors then $1$ and ${\color{green}151}$: $\frac{151}{151} = {\color{red}1}$.

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: $2114 = 2 \cdot 7 \cdot 151$.

The prime factorization is $2114 = 2 \cdot 7 \cdot 151$A.