# Prime factorization of $2550$

The calculator will find the prime factorization of $2550$, with steps shown.

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Find the prime factorization of $2550$.

### Solution

Start with the number $2$.

Determine whether $2550$ is divisible by $2$.

It is divisible, thus, divide $2550$ by ${\color{green}2}$: $\frac{2550}{2} = {\color{red}1275}$.

Determine whether $1275$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1275$ is divisible by $3$.

It is divisible, thus, divide $1275$ by ${\color{green}3}$: $\frac{1275}{3} = {\color{red}425}$.

Determine whether $425$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $425$ is divisible by $5$.

It is divisible, thus, divide $425$ by ${\color{green}5}$: $\frac{425}{5} = {\color{red}85}$.

Determine whether $85$ is divisible by $5$.

It is divisible, thus, divide $85$ by ${\color{green}5}$: $\frac{85}{5} = {\color{red}17}$.

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: $2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17$.

The prime factorization is $2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17$A.