# Prime factorization of $592$

The calculator will find the prime factorization of $592$, with steps shown.

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Find the prime factorization of $592$.

### Solution

Start with the number $2$.

Determine whether $592$ is divisible by $2$.

It is divisible, thus, divide $592$ by ${\color{green}2}$: $\frac{592}{2} = {\color{red}296}$.

Determine whether $296$ is divisible by $2$.

It is divisible, thus, divide $296$ by ${\color{green}2}$: $\frac{296}{2} = {\color{red}148}$.

Determine whether $148$ is divisible by $2$.

It is divisible, thus, divide $148$ by ${\color{green}2}$: $\frac{148}{2} = {\color{red}74}$.

Determine whether $74$ is divisible by $2$.

It is divisible, thus, divide $74$ by ${\color{green}2}$: $\frac{74}{2} = {\color{red}37}$.

The prime number ${\color{green}37}$ has no other factors then $1$ and ${\color{green}37}$: $\frac{37}{37} = {\color{red}1}$.

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: $592 = 2^{4} \cdot 37$.

The prime factorization is $592 = 2^{4} \cdot 37$A.