# Prime factorization of $4770$

The calculator will find the prime factorization of $4770$, with steps shown.

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Find the prime factorization of $4770$.

### Solution

Start with the number $2$.

Determine whether $4770$ is divisible by $2$.

It is divisible, thus, divide $4770$ by ${\color{green}2}$: $\frac{4770}{2} = {\color{red}2385}$.

Determine whether $2385$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2385$ is divisible by $3$.

It is divisible, thus, divide $2385$ by ${\color{green}3}$: $\frac{2385}{3} = {\color{red}795}$.

Determine whether $795$ is divisible by $3$.

It is divisible, thus, divide $795$ by ${\color{green}3}$: $\frac{795}{3} = {\color{red}265}$.

Determine whether $265$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $265$ is divisible by $5$.

It is divisible, thus, divide $265$ by ${\color{green}5}$: $\frac{265}{5} = {\color{red}53}$.

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: $4770 = 2 \cdot 3^{2} \cdot 5 \cdot 53$.

The prime factorization is $4770 = 2 \cdot 3^{2} \cdot 5 \cdot 53$A.