Introduction to Prime Factorization Calculator
Prime factorization calculator is an online free tool that helps you to find the factor of the prime numbers for finding common factors. Our tool helps you to evaluate the prime factors of given numbers in less than a minute.
Our prime divisors calculator is beneficial for students or researchers who want a tool that can calculate the prime factorization problems quickly without doing manual calculations.
What is Prime Factorization
Prime factorization is stated to be used to find factors that are the product of the original number. It expresses the prime number in factor multiplication after calculation. This method is used to find the common factors for getting the greatest common factor or the least multiple factor.
In the factorization method, 1 number can only divide by itself for other numbers like 1*12=12, not 1 so 1 is not a prime number. There are various methods that are used to solve the prime factorization method but the tree factor or division method.
How to Calculate Prime Factors of a Number
Prime factorization of a number can be calculated with the help of the tree factor method or division method. To gain a better understanding of the evaluation process, let’s take a look at how to find factors using the prime factorization calculator.
Prime Factorization Using the Tree Method
In the tree factor method, we take an example so that you can understand how the tree factor method works. For example, find the factor of 125 using the tree method.
Step 1: Write the original number 125 at the top as 125.
Step 2: Start from the smallest number like 2,3,5,... to find the factors and 125 is divisible from 5.
125
/
5
Step 3: Continue this process till all the numbers do not become prime factors.
125
/ \
5 25
/ \
5 5
/
5
Step 4: Recheck your process whether there is any number left which is the product of that number.
Step 5: After getting all the prime factors of 125, the factors are 5, 5, and 5 using the tree method. When you multiply the given prime factor it gives 125 in solution.
Prime Factorization Using Division Method
Prime factorization of a number can be solved with the help of division method which is also used by the prime factoring calculator. At this time, we should understand it through manual calculations. Let's take a look at an example of prime factorization of 90 using the division method to know how the prime divisors calculator solves it in steps,
Step 1: Start with the number 90 and find the smallest prime factor of 90. So, divide 90 by 2.
$$ 90 \div 2 \;=\; 45 $$
Step 2: Now 45 is not divided by 2 until you can use 3 for division
$$ 45 \div 3 \;=\; 15 $$
Step 3: Again divide 15 by 3.
$$ 15 \div 3 \;=\; 5 $$
Step 4: 5 is divided by 5 only
$$ 5 \div 5 \;=\; 1 $$
Step 5: Write all the factor of 90 as
$$ 2 \times 3 \times 3 \times 5 $$
So, the prime factorization of 90 is 2×3^2×5
Prime Factorization of 36
To find the prime factorization of 36 using the prime division method, prime factorization calculator start by dividing 36 by the smallest prime number (2), then proceed with the following number until you cannot divide anymore. Here are all the steps:
It starts with the number 36 and divides by 2.
$$ 36 \div 2 \;=\; 18 $$
The number 18 is also divided by 2.
$$ 18 \div 2 \;=\; 9 $$
Next prime factor calculator divide 9 by the next smallest prime number, which is 3.
$$ 9 \div 3 \;=\; 3 $$
Divide by 3 again by 3, divide so.
$$ 3 \div 3 \;=\; 1 $$
The prime factors of 36 are all the primes used in the division: 2, 2, 3, and 3.
So, the prime factorization of 36 is 2^2×3^2 , which means 36 equals.
If you are tired of doing manual calculations, our Prime Factorization Solver is here to help! With a single click, you can quickly determine the prime factorization of numbers such as 36.
Prime Factorization of 72
To find the solution of prime factorization of 72 with the help of the tree factor method.
Step 1:
It starts with the number 72 and writes it at the top.
72
Step 2:
Find a prime factor of 72 is divisible by 2,which is 72÷2=36
72
/
2
Step 3:
Continue this factoring process and divide 36 by 2 again as 36÷2=18
72
/
2

36
Step 4:
Again 18 is divisible by 2 as 18÷2=9
72
/
2

36
\
18
Step 5:
The factor 9 is divide by 3 as 9÷3=3
72
/
2

36
\
18
\
9
Step 6:
Next Factor 3 is divided by 3 only 3÷3=1
72
/
2

36
\
18
\
9
\
3
Step 7:
the factor tree of 72 is shown as
72
/
2

36
/ \
2 18
/ \
2 9
/ \
3 3
Find the prime factorization of 72 quickly and easily without doing any calculations by using our prime factorisation calculator.
Prime Factorization of 18
For the calculation of the prime factorization of 18, we use the prime division method. You can start with 18 divisions by the smallest prime number 2 until its remainder does not become 1.
18 is divisible by 2 as 18÷2=9.
The next prime factor is 3 which divides 9 as
$$ 9 \div 3 \;=\; 3 $$
Since 3 is divisible by 3.
$$ 3 \div 3 \;=\; 1 $$
The prime factors of 18 are all the prime numbers after divisions 2, 3, and 3.
So, the prime factorization of 18 is 2×3×3, which is written as 2×3^2
How to Find Prime Factors on a Calculator
The prime factor calculator has a simple layout that lets you immediately solve number problems. You do not need to put in any external effort to get a solution, just follow some steps only for the calculation. These steps are:
 Enter the value of the given number in the input box
 Check your input number before clicking on the calculate button to get the correct answer as per your input in the prime factorization calculator.
 Press the “Calculate” button for the solution of a prime factorization question.
Press the “Recalculate” button for more evaluation of the prime factorization examples with the solution.  You can use the load example to do more questions about the prime factorization method to check the accuracy of the solution.
Outcome of Prime Divisors Calculator
Prime factor decomposition calculator gives you a solution according to your given input number. When you click on the calculate button it starts the calculation process. It may include as:
Result Box
You get the solution of Prime factorization questions after clicking on the result button.
Steps Box
Click on the Possible Steps option to get the solution to the given prime factorization question from the calculator using a stepbystep method.
Benefits of Using a Prime Factor Calculator
Prime factorisation calculator gives you several benefits whenever you use it to calculate a given number. Moreover, it is an amazing tool for solving various types of numbers in the prime factors method with the solution. These benefits are;
 It is a reliable tool as it gives you accurate solutions to Prime factorization questions.
 It is a userfriendly tool that allows everyone, even a beginner, to easily solve the given number problem in the prime factorization solver.
 There is no restriction on signing up before using the prime factoring calculator.
 It is a fast tool that provides you with the solution to your given number factors question in a fraction of a second.
 Prime factor decomposition calculator is a free online tool, you can find it for the evaluation of prime number questions without spending anything.
 Prime factorization Calculator used for practice to solve various kinds of examples of prime factorization with solution.