# Prime factorization of $4070$

The calculator will find the prime factorization of $4070$, with steps shown.

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Find the prime factorization of $4070$.

### Solution

Start with the number $2$.

Determine whether $4070$ is divisible by $2$.

It is divisible, thus, divide $4070$ by ${\color{green}2}$: $\frac{4070}{2} = {\color{red}2035}$.

Determine whether $2035$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2035$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2035$ is divisible by $5$.

It is divisible, thus, divide $2035$ by ${\color{green}5}$: $\frac{2035}{5} = {\color{red}407}$.

Determine whether $407$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $407$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $407$ is divisible by $11$.

It is divisible, thus, divide $407$ by ${\color{green}11}$: $\frac{407}{11} = {\color{red}37}$.

The prime number ${\color{green}37}$ has no other factors then $1$ and ${\color{green}37}$: $\frac{37}{37} = {\color{red}1}$.

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: $4070 = 2 \cdot 5 \cdot 11 \cdot 37$.

The prime factorization is $4070 = 2 \cdot 5 \cdot 11 \cdot 37$A.