# Prime factorization of $4514$

The calculator will find the prime factorization of $4514$, with steps shown.

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Find the prime factorization of $4514$.

### Solution

Start with the number $2$.

Determine whether $4514$ is divisible by $2$.

It is divisible, thus, divide $4514$ by ${\color{green}2}$: $\frac{4514}{2} = {\color{red}2257}$.

Determine whether $2257$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2257$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2257$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $2257$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $2257$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $2257$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $2257$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $2257$ is divisible by $19$.

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

The next prime number is $23$.

Determine whether $2257$ is divisible by $23$.

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

The next prime number is $29$.

Determine whether $2257$ is divisible by $29$.

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

The next prime number is $31$.

Determine whether $2257$ is divisible by $31$.

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

The next prime number is $37$.

Determine whether $2257$ is divisible by $37$.

It is divisible, thus, divide $2257$ by ${\color{green}37}$: $\frac{2257}{37} = {\color{red}61}$.

The prime number ${\color{green}61}$ has no other factors then $1$ and ${\color{green}61}$: $\frac{61}{61} = {\color{red}1}$.

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: $4514 = 2 \cdot 37 \cdot 61$.

The prime factorization is $4514 = 2 \cdot 37 \cdot 61$A.