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Prime Factorization Calculator

Prime Factorization Calculator

Input any integer number and the calculator will find all prime factors of that number. Also, you can get a detailed list of all possible prime numbers up to the number provided.

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The prime factorization calculator finds all possible prime factors of an integer and shows factor tree. Enter a number and get Sieve of Eratosthenes and a list of prime numbers before it. Also, this advanced tool tells you whether the given number is prime or not!

What Is Prime Factorization?

“It is the technique of finding the prime numbers that give us the original number on multiplication”

Prime factorization is also known as the decomposition of a composite integer into smaller prime numerals.

Also, you can try this simple and best tool by calculator-online to solve your fractions-related math problems!

What Is The Prime Factor?

“A prime factor is basically a prime number that is only divisible by 1 and itself”

Recognizing a number as prime or composite is not easy when large integers are involved. But the prime factor calculator can handle this intelligently and swiftly tells you what is the nature of the number entered.

How Do You Find The Prime Factorization of a Number?

Let us resolve a couple of examples to elaborate on prime factorization methods:

Factor Tree Method:

How to find prime factorization tree of the number 692.


  • Write 692 at the top of the tree
  • Find two numbers that make 692 on multiplication. In our case, these are 346 and 2. Write these numbers as branches of the original number
  • Now look if any of the branch numbers is a composite number. In our case, it is 346.
  • Reduce 346 into daughter branches as 173 and 2
  • As 173 and 2 are prime factors, just stop here as this is our final solution
Prime Factor Tree:

|       \
346   2
|           \
173        2

Making factor trees is a good way of doing prime factorization that displays all the factors in a simple form. The use of prime factor tree calculator might be very helpful and time-saving for this purpose.

Prime Decomposition (Factors and Exponents):

Represent 50 as the prime exponents of it.


|     \
25    2
|          \
5           5

So we have:

50 = 2 * 5 * 5

50 = 2 * \(5^{2}\)

Prime factorization calculator has the ability to display exponents of factors so that you can handle your calculation without any error.

Trial Division Method:

In this method, if you have to find the prime factors of 50, then you have to start by checking each integer that how often it will divide 50. The subsequent set will be of prime factors that will give us 50 on multiplication.


2 multiplied by 5 and 5 multiplied by 5 again will give us 50 so the prime factors of 50 are 2, 5, and 5. In the simplest way, you can do the following procedure:

50/2 = 25

25/5 = 5

5/5 = 1

However, the calculation might get long in this way so you can use factored form calculator for your convenience.

Working of Prime Factorization Calculator:

Our prime power factorization calculator makes your prime factor calculations fast and accurate. Let’s find out how!


  • Select the mode of the calculator from the top list
  • After that, enter the number in the designated field
  • Tap Calculate


  • Prime factorization corresponding to the given number
  • Exponential form of the given input
  • Comma-separated values (CSV) format for the given value
  • All factors of the given number
  • Prime factor tree
  • Sieve of Eratosthenes (table)
  • Positive prime numbers smaller than the number of your choice
  • Whether the number of your choice is a prime number or not
  • Previous & Nearest prime number


What Is The Difference Between Prime Numbers & Composite Numbers?

A prime number is a term that refers to all those numbers that cannot be made by multiplying different whole numbers.

For example;

1, 2, 3, 5, 7, 11, …

The composite numbers can be formed by multiplying different whole numbers.

For example;

4, 6, 9, 10, 12, 14, …

What Is The Prime Factorization of 2020?

2020 = 2^2 × 5 × 101

As it has a total of 4 prime factors, 2020 is said to be a composite number.

What Is The Least Factor of a Number?

The least prime factor of an integer “n” is said to be the smallest prime number, which divides the number.

What Is The Sum of All Prime Numbers?

As there are infinite prime numbers, their sum will also be infinite.

Prime Factorization of Numbers:

Number Prime Factor
100 2 × 2 × 5 × 5
2 2 itself is a prime number
10 2 × 5
5 5 itself is a prime number
3 3 itself is a prime number
36 2 × 2 × 3 × 3
24 2 × 2 × 2 × 3
60 2 × 2 × 3 × 5
18 2 × 3 × 3
72 2 × 2 × 2 × 3 × 3
45 3 × 3 × 5
40 2 × 2 × 2 × 5
50 2 × 5 × 5
48 2 × 2 × 2 × 2 × 3
30 2 × 3 × 5
42 2 × 3 × 7
72 2 × 2 × 2 × 3 × 3

All of the above factors have been cross-checked by the prime factorization calculator so that you may not feel trouble while figuring out prime factors manually.


From the source of Wikipedia: About Factorization – Integers Factorization and general methods

From the source of study: how to find prime factorization of a Number (Chapter 1 / Lesson 2)

From the source of brilliant: Learn about the Sieve of Eratosthenes (simple and ancient algorithm used to find the prime numbers up to any provided limit)

From the source of helpingwithmath: Prime Factorization (make a Factor Trees) – the simple prime factorization tree calculator also helps you to create factor tree for the number of your choice.