# Prime Factorization Calculator

This calculator will find the prime factorization of the given number, with steps shown.

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Find the prime factorization of $$75$$$. ## Solution Start with the number $$2$$$.

Determine whether $$75$$$is divisible by $$2$$$.

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

The next prime number is $$3$$$. Determine whether $$75$$$ is divisible by $$3$$$. It is divisible, thus, divide $$75$$$ by $$\color{green}{3}$$$: $$\frac{75}{3} = \color{red}{25}$$$.

Determine whether $$25$$$is divisible by $$3$$$.

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

The next prime number is $$5$$$. Determine whether $$25$$$ is divisible by $$5$$$. It is divisible, thus, divide $$25$$$ by $$\color{green}{5}$$$: $$\frac{25}{5} = \color{red}{5}$$$.

The prime number $$\color{green}{5}$$$has no other factors then $$1$$$ and $$\color{green}{5}$$$: $$\frac{5}{5} = \color{red}{1}$$$.

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: $$75 = 3 \cdot 5^{2}$$$.

The prime factorization is $$75 = 3 \cdot 5^{2}$$\$A.