# Prime factorization of $4823$

The calculator will find the prime factorization of $4823$, with steps shown.

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Find the prime factorization of $4823$.

### Solution

Start with the number $2$.

Determine whether $4823$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4823$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $4823$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $4823$ is divisible by $7$.

It is divisible, thus, divide $4823$ by ${\color{green}7}$: $\frac{4823}{7} = {\color{red}689}$.

Determine whether $689$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $689$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $689$ is divisible by $13$.

It is divisible, thus, divide $689$ by ${\color{green}13}$: $\frac{689}{13} = {\color{red}53}$.

The prime number ${\color{green}53}$ has no other factors then $1$ and ${\color{green}53}$: $\frac{53}{53} = {\color{red}1}$.

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: $4823 = 7 \cdot 13 \cdot 53$.

The prime factorization is $4823 = 7 \cdot 13 \cdot 53$A.