# Prime factorization of $2784$

The calculator will find the prime factorization of $2784$, with steps shown.

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Find the prime factorization of $2784$.

### Solution

Start with the number $2$.

Determine whether $2784$ is divisible by $2$.

It is divisible, thus, divide $2784$ by ${\color{green}2}$: $\frac{2784}{2} = {\color{red}1392}$.

Determine whether $1392$ is divisible by $2$.

It is divisible, thus, divide $1392$ by ${\color{green}2}$: $\frac{1392}{2} = {\color{red}696}$.

Determine whether $696$ is divisible by $2$.

It is divisible, thus, divide $696$ by ${\color{green}2}$: $\frac{696}{2} = {\color{red}348}$.

Determine whether $348$ is divisible by $2$.

It is divisible, thus, divide $348$ by ${\color{green}2}$: $\frac{348}{2} = {\color{red}174}$.

Determine whether $174$ is divisible by $2$.

It is divisible, thus, divide $174$ by ${\color{green}2}$: $\frac{174}{2} = {\color{red}87}$.

Determine whether $87$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $87$ is divisible by $3$.

It is divisible, thus, divide $87$ by ${\color{green}3}$: $\frac{87}{3} = {\color{red}29}$.

The prime number ${\color{green}29}$ has no other factors then $1$ and ${\color{green}29}$: $\frac{29}{29} = {\color{red}1}$.

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: $2784 = 2^{5} \cdot 3 \cdot 29$.

The prime factorization is $2784 = 2^{5} \cdot 3 \cdot 29$A.