# Prime factorization of $4825$

The calculator will find the prime factorization of $4825$, with steps shown.

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Find the prime factorization of $4825$.

### Solution

Start with the number $2$.

Determine whether $4825$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4825$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $4825$ is divisible by $5$.

It is divisible, thus, divide $4825$ by ${\color{green}5}$: $\frac{4825}{5} = {\color{red}965}$.

Determine whether $965$ is divisible by $5$.

It is divisible, thus, divide $965$ by ${\color{green}5}$: $\frac{965}{5} = {\color{red}193}$.

The prime number ${\color{green}193}$ has no other factors then $1$ and ${\color{green}193}$: $\frac{193}{193} = {\color{red}1}$.

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: $4825 = 5^{2} \cdot 193$.

The prime factorization is $4825 = 5^{2} \cdot 193$A.