# Prime factorization of $4074$

The calculator will find the prime factorization of $4074$, with steps shown.

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Find the prime factorization of $4074$.

### Solution

Start with the number $2$.

Determine whether $4074$ is divisible by $2$.

It is divisible, thus, divide $4074$ by ${\color{green}2}$: $\frac{4074}{2} = {\color{red}2037}$.

Determine whether $2037$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2037$ is divisible by $3$.

It is divisible, thus, divide $2037$ by ${\color{green}3}$: $\frac{2037}{3} = {\color{red}679}$.

Determine whether $679$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $679$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $679$ is divisible by $7$.

It is divisible, thus, divide $679$ by ${\color{green}7}$: $\frac{679}{7} = {\color{red}97}$.

The prime number ${\color{green}97}$ has no other factors then $1$ and ${\color{green}97}$: $\frac{97}{97} = {\color{red}1}$.

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: $4074 = 2 \cdot 3 \cdot 7 \cdot 97$.

The prime factorization is $4074 = 2 \cdot 3 \cdot 7 \cdot 97$A.