# Prime factorization of $4275$

The calculator will find the prime factorization of $4275$, with steps shown.

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Find the prime factorization of $4275$.

### Solution

Start with the number $2$.

Determine whether $4275$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4275$ is divisible by $3$.

It is divisible, thus, divide $4275$ by ${\color{green}3}$: $\frac{4275}{3} = {\color{red}1425}$.

Determine whether $1425$ is divisible by $3$.

It is divisible, thus, divide $1425$ by ${\color{green}3}$: $\frac{1425}{3} = {\color{red}475}$.

Determine whether $475$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $475$ is divisible by $5$.

It is divisible, thus, divide $475$ by ${\color{green}5}$: $\frac{475}{5} = {\color{red}95}$.

Determine whether $95$ is divisible by $5$.

It is divisible, thus, divide $95$ by ${\color{green}5}$: $\frac{95}{5} = {\color{red}19}$.

The prime number ${\color{green}19}$ has no other factors then $1$ and ${\color{green}19}$: $\frac{19}{19} = {\color{red}1}$.

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: $4275 = 3^{2} \cdot 5^{2} \cdot 19$.

The prime factorization is $4275 = 3^{2} \cdot 5^{2} \cdot 19$A.