# Prime factorization of $2601$

The calculator will find the prime factorization of $2601$, with steps shown.

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Find the prime factorization of $2601$.

### Solution

Start with the number $2$.

Determine whether $2601$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2601$ is divisible by $3$.

It is divisible, thus, divide $2601$ by ${\color{green}3}$: $\frac{2601}{3} = {\color{red}867}$.

Determine whether $867$ is divisible by $3$.

It is divisible, thus, divide $867$ by ${\color{green}3}$: $\frac{867}{3} = {\color{red}289}$.

Determine whether $289$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $289$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $289$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $289$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $289$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $289$ is divisible by $17$.

It is divisible, thus, divide $289$ by ${\color{green}17}$: $\frac{289}{17} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $2601 = 3^{2} \cdot 17^{2}$.

The prime factorization is $2601 = 3^{2} \cdot 17^{2}$A.