# Prime factorization of $2992$

The calculator will find the prime factorization of $2992$, with steps shown.

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Find the prime factorization of $2992$.

### Solution

Start with the number $2$.

Determine whether $2992$ is divisible by $2$.

It is divisible, thus, divide $2992$ by ${\color{green}2}$: $\frac{2992}{2} = {\color{red}1496}$.

Determine whether $1496$ is divisible by $2$.

It is divisible, thus, divide $1496$ by ${\color{green}2}$: $\frac{1496}{2} = {\color{red}748}$.

Determine whether $748$ is divisible by $2$.

It is divisible, thus, divide $748$ by ${\color{green}2}$: $\frac{748}{2} = {\color{red}374}$.

Determine whether $374$ is divisible by $2$.

It is divisible, thus, divide $374$ by ${\color{green}2}$: $\frac{374}{2} = {\color{red}187}$.

Determine whether $187$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $187$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $187$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $187$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $187$ is divisible by $11$.

It is divisible, thus, divide $187$ by ${\color{green}11}$: $\frac{187}{11} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $2992 = 2^{4} \cdot 11 \cdot 17$.

The prime factorization is $2992 = 2^{4} \cdot 11 \cdot 17$A.