# Prime factorization of $4796$

The calculator will find the prime factorization of $4796$, with steps shown.

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Find the prime factorization of $4796$.

### Solution

Start with the number $2$.

Determine whether $4796$ is divisible by $2$.

It is divisible, thus, divide $4796$ by ${\color{green}2}$: $\frac{4796}{2} = {\color{red}2398}$.

Determine whether $2398$ is divisible by $2$.

It is divisible, thus, divide $2398$ by ${\color{green}2}$: $\frac{2398}{2} = {\color{red}1199}$.

Determine whether $1199$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1199$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1199$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1199$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $1199$ is divisible by $11$.

It is divisible, thus, divide $1199$ by ${\color{green}11}$: $\frac{1199}{11} = {\color{red}109}$.

The prime number ${\color{green}109}$ has no other factors then $1$ and ${\color{green}109}$: $\frac{109}{109} = {\color{red}1}$.

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: $4796 = 2^{2} \cdot 11 \cdot 109$.

The prime factorization is $4796 = 2^{2} \cdot 11 \cdot 109$A.