# Prime factorization of $2074$

The calculator will find the prime factorization of $2074$, with steps shown.

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Find the prime factorization of $2074$.

### Solution

Start with the number $2$.

Determine whether $2074$ is divisible by $2$.

It is divisible, thus, divide $2074$ by ${\color{green}2}$: $\frac{2074}{2} = {\color{red}1037}$.

Determine whether $1037$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1037$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1037$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1037$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $1037$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $1037$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $1037$ is divisible by $17$.

It is divisible, thus, divide $1037$ by ${\color{green}17}$: $\frac{1037}{17} = {\color{red}61}$.

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: $2074 = 2 \cdot 17 \cdot 61$.

The prime factorization is $2074 = 2 \cdot 17 \cdot 61$A.