# Prime factorization of $3500$

The calculator will find the prime factorization of $3500$, 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 $3500$.

### Solution

Start with the number $2$.

Determine whether $3500$ is divisible by $2$.

It is divisible, thus, divide $3500$ by ${\color{green}2}$: $\frac{3500}{2} = {\color{red}1750}$.

Determine whether $1750$ is divisible by $2$.

It is divisible, thus, divide $1750$ by ${\color{green}2}$: $\frac{1750}{2} = {\color{red}875}$.

Determine whether $875$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $875$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $875$ is divisible by $5$.

It is divisible, thus, divide $875$ by ${\color{green}5}$: $\frac{875}{5} = {\color{red}175}$.

Determine whether $175$ is divisible by $5$.

It is divisible, thus, divide $175$ by ${\color{green}5}$: $\frac{175}{5} = {\color{red}35}$.

Determine whether $35$ is divisible by $5$.

It is divisible, thus, divide $35$ by ${\color{green}5}$: $\frac{35}{5} = {\color{red}7}$.

The prime number ${\color{green}7}$ has no other factors then $1$ and ${\color{green}7}$: $\frac{7}{7} = {\color{red}1}$.

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: $3500 = 2^{2} \cdot 5^{3} \cdot 7$.

The prime factorization is $3500 = 2^{2} \cdot 5^{3} \cdot 7$A.