# Prime factorization of $4095$

The calculator will find the prime factorization of $4095$, with steps shown.

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Find the prime factorization of $4095$.

### Solution

Start with the number $2$.

Determine whether $4095$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4095$ is divisible by $3$.

It is divisible, thus, divide $4095$ by ${\color{green}3}$: $\frac{4095}{3} = {\color{red}1365}$.

Determine whether $1365$ is divisible by $3$.

It is divisible, thus, divide $1365$ by ${\color{green}3}$: $\frac{1365}{3} = {\color{red}455}$.

Determine whether $455$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $455$ is divisible by $5$.

It is divisible, thus, divide $455$ by ${\color{green}5}$: $\frac{455}{5} = {\color{red}91}$.

Determine whether $91$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $91$ is divisible by $7$.

It is divisible, thus, divide $91$ by ${\color{green}7}$: $\frac{91}{7} = {\color{red}13}$.

The prime number ${\color{green}13}$ has no other factors then $1$ and ${\color{green}13}$: $\frac{13}{13} = {\color{red}1}$.

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: $4095 = 3^{2} \cdot 5 \cdot 7 \cdot 13$.

The prime factorization is $4095 = 3^{2} \cdot 5 \cdot 7 \cdot 13$A.