# Prime factorization of $3476$

The calculator will find the prime factorization of $3476$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $3476$.

### Solution

Start with the number $2$.

Determine whether $3476$ is divisible by $2$.

It is divisible, thus, divide $3476$ by ${\color{green}2}$: $\frac{3476}{2} = {\color{red}1738}$.

Determine whether $1738$ is divisible by $2$.

It is divisible, thus, divide $1738$ by ${\color{green}2}$: $\frac{1738}{2} = {\color{red}869}$.

Determine whether $869$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $869$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $869$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $869$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $869$ is divisible by $11$.

It is divisible, thus, divide $869$ by ${\color{green}11}$: $\frac{869}{11} = {\color{red}79}$.

The prime number ${\color{green}79}$ has no other factors then $1$ and ${\color{green}79}$: $\frac{79}{79} = {\color{red}1}$.

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: $3476 = 2^{2} \cdot 11 \cdot 79$.

The prime factorization is $3476 = 2^{2} \cdot 11 \cdot 79$A.