# Prime factorization of $2149$

The calculator will find the prime factorization of $2149$, with steps shown.

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Find the prime factorization of $2149$.

### Solution

Start with the number $2$.

Determine whether $2149$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2149$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2149$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $2149$ is divisible by $7$.

It is divisible, thus, divide $2149$ by ${\color{green}7}$: $\frac{2149}{7} = {\color{red}307}$.

The prime number ${\color{green}307}$ has no other factors then $1$ and ${\color{green}307}$: $\frac{307}{307} = {\color{red}1}$.

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: $2149 = 7 \cdot 307$.

The prime factorization is $2149 = 7 \cdot 307$A.