# Prime factorization of $650$

The calculator will find the prime factorization of $650$, with steps shown.

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Find the prime factorization of $650$.

### Solution

Start with the number $2$.

Determine whether $650$ is divisible by $2$.

It is divisible, thus, divide $650$ by ${\color{green}2}$: $\frac{650}{2} = {\color{red}325}$.

Determine whether $325$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $325$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $325$ is divisible by $5$.

It is divisible, thus, divide $325$ by ${\color{green}5}$: $\frac{325}{5} = {\color{red}65}$.

Determine whether $65$ is divisible by $5$.

It is divisible, thus, divide $65$ by ${\color{green}5}$: $\frac{65}{5} = {\color{red}13}$.

The prime number ${\color{green}13}$ has no other factors then $1$ and ${\color{green}13}$: $\frac{13}{13} = {\color{red}1}$.

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: $650 = 2 \cdot 5^{2} \cdot 13$.

The prime factorization is $650 = 2 \cdot 5^{2} \cdot 13$A.