Prime Factorization Calculator
This calculator will find the prime factorization of the given number, with steps shown.
Your Input
Find the prime factorization of $$$75$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$75$$$ is divisible by $$$2$$$.
Since it is not divisible, 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, 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: $$$75 = 3 \cdot 5^{2}$$$.