# Prime factorization of $1128$

The calculator will find the prime factorization of $1128$, with steps shown.

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Find the prime factorization of $1128$.

### Solution

Start with the number $2$.

Determine whether $1128$ is divisible by $2$.

It is divisible, thus, divide $1128$ by ${\color{green}2}$: $\frac{1128}{2} = {\color{red}564}$.

Determine whether $564$ is divisible by $2$.

It is divisible, thus, divide $564$ by ${\color{green}2}$: $\frac{564}{2} = {\color{red}282}$.

Determine whether $282$ is divisible by $2$.

It is divisible, thus, divide $282$ by ${\color{green}2}$: $\frac{282}{2} = {\color{red}141}$.

Determine whether $141$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $141$ is divisible by $3$.

It is divisible, thus, divide $141$ by ${\color{green}3}$: $\frac{141}{3} = {\color{red}47}$.

The prime number ${\color{green}47}$ has no other factors then $1$ and ${\color{green}47}$: $\frac{47}{47} = {\color{red}1}$.

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: $1128 = 2^{3} \cdot 3 \cdot 47$.

The prime factorization is $1128 = 2^{3} \cdot 3 \cdot 47$A.