# Prime factorization of $3460$

The calculator will find the prime factorization of $3460$, with steps shown.

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Find the prime factorization of $3460$.

### Solution

Start with the number $2$.

Determine whether $3460$ is divisible by $2$.

It is divisible, thus, divide $3460$ by ${\color{green}2}$: $\frac{3460}{2} = {\color{red}1730}$.

Determine whether $1730$ is divisible by $2$.

It is divisible, thus, divide $1730$ by ${\color{green}2}$: $\frac{1730}{2} = {\color{red}865}$.

Determine whether $865$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $865$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $865$ is divisible by $5$.

It is divisible, thus, divide $865$ by ${\color{green}5}$: $\frac{865}{5} = {\color{red}173}$.

The prime number ${\color{green}173}$ has no other factors then $1$ and ${\color{green}173}$: $\frac{173}{173} = {\color{red}1}$.

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: $3460 = 2^{2} \cdot 5 \cdot 173$.

The prime factorization is $3460 = 2^{2} \cdot 5 \cdot 173$A.