# Prime factorization of $1225$

The calculator will find the prime factorization of $1225$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $1225$.

### Solution

Start with the number $2$.

Determine whether $1225$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1225$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1225$ is divisible by $5$.

It is divisible, thus, divide $1225$ by ${\color{green}5}$: $\frac{1225}{5} = {\color{red}245}$.

Determine whether $245$ is divisible by $5$.

It is divisible, thus, divide $245$ by ${\color{green}5}$: $\frac{245}{5} = {\color{red}49}$.

Determine whether $49$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $49$ is divisible by $7$.

It is divisible, thus, divide $49$ by ${\color{green}7}$: $\frac{49}{7} = {\color{red}7}$.

The prime number ${\color{green}7}$ has no other factors then $1$ and ${\color{green}7}$: $\frac{7}{7} = {\color{red}1}$.

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: $1225 = 5^{2} \cdot 7^{2}$.

The prime factorization is $1225 = 5^{2} \cdot 7^{2}$A.