# Prime factorization of $4575$

The calculator will find the prime factorization of $4575$, with steps shown.

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Find the prime factorization of $4575$.

### Solution

Start with the number $2$.

Determine whether $4575$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4575$ is divisible by $3$.

It is divisible, thus, divide $4575$ by ${\color{green}3}$: $\frac{4575}{3} = {\color{red}1525}$.

Determine whether $1525$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1525$ is divisible by $5$.

It is divisible, thus, divide $1525$ by ${\color{green}5}$: $\frac{1525}{5} = {\color{red}305}$.

Determine whether $305$ is divisible by $5$.

It is divisible, thus, divide $305$ by ${\color{green}5}$: $\frac{305}{5} = {\color{red}61}$.

The prime number ${\color{green}61}$ has no other factors then $1$ and ${\color{green}61}$: $\frac{61}{61} = {\color{red}1}$.

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: $4575 = 3 \cdot 5^{2} \cdot 61$.

The prime factorization is $4575 = 3 \cdot 5^{2} \cdot 61$A.