# Prime factorization of $275$

The calculator will find the prime factorization of $275$, with steps shown.

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Find the prime factorization of $275$.

### Solution

Start with the number $2$.

Determine whether $275$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $275$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $275$ is divisible by $5$.

It is divisible, thus, divide $275$ by ${\color{green}5}$: $\frac{275}{5} = {\color{red}55}$.

Determine whether $55$ is divisible by $5$.

It is divisible, thus, divide $55$ by ${\color{green}5}$: $\frac{55}{5} = {\color{red}11}$.

The prime number ${\color{green}11}$ has no other factors then $1$ and ${\color{green}11}$: $\frac{11}{11} = {\color{red}1}$.

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: $275 = 5^{2} \cdot 11$.

The prime factorization is $275 = 5^{2} \cdot 11$A.