# Prime factorization of $2527$

The calculator will find the prime factorization of $2527$, with steps shown.

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Find the prime factorization of $2527$.

### Solution

Start with the number $2$.

Determine whether $2527$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2527$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2527$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $2527$ is divisible by $7$.

It is divisible, thus, divide $2527$ by ${\color{green}7}$: $\frac{2527}{7} = {\color{red}361}$.

Determine whether $361$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $361$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $361$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $361$ is divisible by $17$.

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

The next prime number is $19$.

Determine whether $361$ is divisible by $19$.

It is divisible, thus, divide $361$ by ${\color{green}19}$: $\frac{361}{19} = {\color{red}19}$.

The prime number ${\color{green}19}$ has no other factors then $1$ and ${\color{green}19}$: $\frac{19}{19} = {\color{red}1}$.

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: $2527 = 7 \cdot 19^{2}$.

The prime factorization is $2527 = 7 \cdot 19^{2}$A.