# Prime factorization of $4564$

The calculator will find the prime factorization of $4564$, with steps shown.

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Find the prime factorization of $4564$.

### Solution

Start with the number $2$.

Determine whether $4564$ is divisible by $2$.

It is divisible, thus, divide $4564$ by ${\color{green}2}$: $\frac{4564}{2} = {\color{red}2282}$.

Determine whether $2282$ is divisible by $2$.

It is divisible, thus, divide $2282$ by ${\color{green}2}$: $\frac{2282}{2} = {\color{red}1141}$.

Determine whether $1141$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1141$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1141$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1141$ is divisible by $7$.

It is divisible, thus, divide $1141$ by ${\color{green}7}$: $\frac{1141}{7} = {\color{red}163}$.

The prime number ${\color{green}163}$ has no other factors then $1$ and ${\color{green}163}$: $\frac{163}{163} = {\color{red}1}$.

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: $4564 = 2^{2} \cdot 7 \cdot 163$.

The prime factorization is $4564 = 2^{2} \cdot 7 \cdot 163$A.