# Prime factorization of $4225$

The calculator will find the prime factorization of $4225$, with steps shown.

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Find the prime factorization of $4225$.

### Solution

Start with the number $2$.

Determine whether $4225$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4225$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $4225$ is divisible by $5$.

It is divisible, thus, divide $4225$ by ${\color{green}5}$: $\frac{4225}{5} = {\color{red}845}$.

Determine whether $845$ is divisible by $5$.

It is divisible, thus, divide $845$ by ${\color{green}5}$: $\frac{845}{5} = {\color{red}169}$.

Determine whether $169$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $169$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $169$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $169$ is divisible by $13$.

It is divisible, thus, divide $169$ by ${\color{green}13}$: $\frac{169}{13} = {\color{red}13}$.

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: $4225 = 5^{2} \cdot 13^{2}$.

The prime factorization is $4225 = 5^{2} \cdot 13^{2}$A.