# Prime factorization of $4544$

The calculator will find the prime factorization of $4544$, with steps shown.

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Find the prime factorization of $4544$.

### Solution

Start with the number $2$.

Determine whether $4544$ is divisible by $2$.

It is divisible, thus, divide $4544$ by ${\color{green}2}$: $\frac{4544}{2} = {\color{red}2272}$.

Determine whether $2272$ is divisible by $2$.

It is divisible, thus, divide $2272$ by ${\color{green}2}$: $\frac{2272}{2} = {\color{red}1136}$.

Determine whether $1136$ is divisible by $2$.

It is divisible, thus, divide $1136$ by ${\color{green}2}$: $\frac{1136}{2} = {\color{red}568}$.

Determine whether $568$ is divisible by $2$.

It is divisible, thus, divide $568$ by ${\color{green}2}$: $\frac{568}{2} = {\color{red}284}$.

Determine whether $284$ is divisible by $2$.

It is divisible, thus, divide $284$ by ${\color{green}2}$: $\frac{284}{2} = {\color{red}142}$.

Determine whether $142$ is divisible by $2$.

It is divisible, thus, divide $142$ by ${\color{green}2}$: $\frac{142}{2} = {\color{red}71}$.

The prime number ${\color{green}71}$ has no other factors then $1$ and ${\color{green}71}$: $\frac{71}{71} = {\color{red}1}$.

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: $4544 = 2^{6} \cdot 71$.

The prime factorization is $4544 = 2^{6} \cdot 71$A.