# Prime factorization of $4565$

The calculator will find the prime factorization of $4565$, with steps shown.

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Find the prime factorization of $4565$.

### Solution

Start with the number $2$.

Determine whether $4565$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4565$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $4565$ is divisible by $5$.

It is divisible, thus, divide $4565$ by ${\color{green}5}$: $\frac{4565}{5} = {\color{red}913}$.

Determine whether $913$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $913$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $913$ is divisible by $11$.

It is divisible, thus, divide $913$ by ${\color{green}11}$: $\frac{913}{11} = {\color{red}83}$.

The prime number ${\color{green}83}$ has no other factors then $1$ and ${\color{green}83}$: $\frac{83}{83} = {\color{red}1}$.

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: $4565 = 5 \cdot 11 \cdot 83$.

The prime factorization is $4565 = 5 \cdot 11 \cdot 83$A.