# Prime factorization of $4510$

The calculator will find the prime factorization of $4510$, with steps shown.

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Find the prime factorization of $4510$.

### Solution

Start with the number $2$.

Determine whether $4510$ is divisible by $2$.

It is divisible, thus, divide $4510$ by ${\color{green}2}$: $\frac{4510}{2} = {\color{red}2255}$.

Determine whether $2255$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2255$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2255$ is divisible by $5$.

It is divisible, thus, divide $2255$ by ${\color{green}5}$: $\frac{2255}{5} = {\color{red}451}$.

Determine whether $451$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $451$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $451$ is divisible by $11$.

It is divisible, thus, divide $451$ by ${\color{green}11}$: $\frac{451}{11} = {\color{red}41}$.

The prime number ${\color{green}41}$ has no other factors then $1$ and ${\color{green}41}$: $\frac{41}{41} = {\color{red}1}$.

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: $4510 = 2 \cdot 5 \cdot 11 \cdot 41$.

The prime factorization is $4510 = 2 \cdot 5 \cdot 11 \cdot 41$A.