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Prime Factorisation Calculator

Prime Factorisation Calculator used to calculate the prime factorisation of the number you enter here. (Numbers above 10 million may or may not time out. When you have to find out the Prime Factorisation of very large numbers, the Prime Factorisation Calculator can be very handy and useful.

Please type a positive integer number and hit 'Calculate Factors' button find the prime factors.

Ex: Prime Factors of 25 (or) Prime Factors of 46 (or) Prime Factors of 57

Factors of:

Here are some samples of Prime Factorisation calculations.


Related Calculators:

Table of Factors from 1 to 100


Number Factors Prime or Composite
1 1 Neither prime nor composite
2 1, 2 Prime
3 1, 3 Prime
4 1, 2, 4 Composite
5 1, 5 Prime
6 1, 2, 3, 6 Composite
7 1, 7 Prime
8 1, 2, 4, 8 Composite
9 1, 3, 9 Composite
10 1, 2, 5, 10 Composite
11 1, 11 Prime
12 1, 2, 3, 4, 6, 12 Composite
13 1, 13 Prime
14 1, 2, 7, 14 Composite
15 1, 3, 5, 15 Composite
16 1, 2, 4, 8, 16 Composite
17 1, 17 Prime
18 1, 2, 3, 6, 9, 18 Composite
19 1, 19 Prime
20 1, 2, 4, 5, 10, 20 Composite
21 1, 3, 7, 21 Composite
22 1, 2, 11, 22 Composite
23 1, 23 Prime
24 1, 2, 3, 4, 6, 8, 12, 24 Composite
25 1, 5, 25 Composite
26 1, 2, 13, 26 Composite
27 1, 3, 9, 27 Composite
28 1, 2, 4, 7, 14, 28 Composite
29 1, 29 Prime
30 1, 2, 3, 5, 6, 10, 15, 30 Composite
31 1, 31 Prime
32 1, 2, 4, 8, 16, 32 Composite
33 1, 3, 11, 33 Composite
34 1, 2, 17, 34 Composite
35 1, 5, 7, 35 Composite
36 1, 2, 3, 4, 6, 9, 12, 18, 36 Composite
37 1, 37 Prime
38 1, 2, 19, 38 Composite
39 1, 3, 13, 39 Composite
40 1, 2, 4, 5, 8, 10, 20, 40 Composite
41 1, 41 Prime
42 1, 2, 3, 6, 7, 14, 21, 42 Composite
43 1, 43 Prime
44 1, 2, 4, 11, 22, 44 Composite
45 1, 3, 5, 9, 15, 45 Composite
46 1, 2, 23, 46 Composite
47 1, 47 Prime
48 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Composite
49 1, 7, 49 Composite
50 1, 2, 5, 10, 25, 50 Composite
51 1, 3, 17, 51 Composite
52 1, 2, 4, 13, 26, 52 Composite
53 1, 53 Prime
54 1, 2, 3, 6, 9, 18, 27, 54 Composite
55 1, 5, 11, 55 Composite
56 1, 2, 4, 7, 8, 14, 28, 56 Composite
57 1, 3, 19, 57 Composite
58 1, 2, 29, 58 Composite
59 1, 59 Prime
60 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Composite
61 1, 61 Prime
62 1, 2, 31, 62 Composite
63 1, 3, 7, 9, 21, 63 Composite
64 1, 2, 4, 8, 16, 32, 64 Composite
65 1, 5, 13, 65 Composite
66 1, 2, 3, 6, 11, 22, 33, 66 Composite
67 1, 67 Prime
68 1, 2, 4, 17, 34, 68 Composite
69 1, 3, 23, 69 Composite
70 1, 2, 5, 7, 10, 14, 35, 70 Composite
71 1, 71 Prime
72 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Composite
73 1, 73 Prime
74 1, 2, 37, 74 Composite
75 1, 3, 5, 15, 25, 75 Composite
76 1, 2, 4, 19, 38, 76 Composite
77 1, 7, 11, 77 Composite
78 1, 2, 3, 6, 13, 26, 39, 78 Composite
79 1, 79 Prime
80 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 Composite
81 1, 3, 9, 27, 81 Composite
82 1, 2, 41, 82 Composite
83 1, 83 Prime
84 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 Composite
85 1, 5, 17, 85 Composite
86 1, 2, 43, 86 Composite
87 1, 3, 29, 87 Composite
88 1, 2, 4, 8, 11, 22, 44, 88 Composite
89 1, 89 Prime
90 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 Composite
91 1, 7, 13, 91 Composite
92 1, 2, 4, 23, 46, 92 Composite
93 1, 3, 31, 93 Composite
94 1, 2, 47, 94 Composite
95 1, 5, 19, 95 Composite
96 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 Composite
97 1, 97 Prime
98 1, 2, 7, 14, 49, 98 Composite
99 1, 3, 9, 11, 33, 99 Composite
100 1, 2, 4, 5, 10, 20, 25, 50, 100 Composite

The prime factorisation calculator can help you to find prime factors of any integer number up to 1 trillion. Just enter the number here in the calculator and within no time you’ll get the prime factorisation.

Prime Factorisation Calculator various applications:

  • Check Prime factors of an integer number up to 1 trillion
  • Also, it can check either a number is prime or not
  • Prime decomposition in an exponential way
  • Make a list of all positive prime numbers smaller than the number you entered and calculate them
  • Comma-separated Values (CSV) of prime factors

To know the complete process, first of all, you must know all about what is a prime number?

A prime number is a positive whole number that is greater than 1 and that can be divided equally just by one and by itself. We can also say that cannot be achieved by multiplying 2 smaller numbers than that. Like 7 is a prime number! You can divide it by 1 or 7 only.

if an integer number is small then it’s very simple to decide whether a number is prime or not. For small numbers, we can use the rules of divisibility and trial division manually. But what if a number is very large and we have to determine whether it is prime or not. It is hard to check it manually as factoring large numbers carry very large primes. In such situations, an online calculator is the best to choose.

What is the prime factor?

Factors of prime numbers are prime factors. So here if we consider the factors of 12, that is, we need to get what integer numbers multiply to provide you 12. We understand that 1 x 12 = 12, 2 x 6 = 12 and 3 x 4 = 12. But here 12, 6, and 4 are not prime factors. The only prime factors of 12 are 2 and 3. You can also check prime factors using a factor calculator.

What is Prime Factorisation?

Any whole number can be uniquely described as the list of prime numbers and such representation is named the prime factorisation, or canonical representation or integer factorisation or prime decomposition. There is exactly one prime factorisation for any positive integer number, and such positive integer has just 1 prime factorisation.

How to Find Prime Factorisation of a Number?

There are various processes to find out the Prime Factorisation of a Number and you can choose any of one as per the need. Here, we try to include two of the methods of prime factorisation:

  1. Trial division
  2. Using prime factors trees.

Trial Division

One of the methods to check the Prime Factor of a number is trial division. Trial division consists of very easy and basic algorithms, though it is an extremely slow process. In this method, we have to check each number by dividing the composite number in question by the integer and deciding if, and how many times, the number can divide the number equally.

To make it more understandable, let go through an example:

To get the prime factorisation of 48, we have to start with dividing it by the smallest prime 2

48 ÷ 2 = 24

24 ÷ 2 = 12

12 ÷ 2 = 6

6 ÷ 2 = 3

But, we can’t divide 3 by 2, but we can divide 3 by itself only

3 ÷ 3 = 1

So here he prime factorisation of 48 = 2 X 2 X 2 X 2 X 3 = 24 X 3

We can check it in a prime factorisation calculator also. The algorithm used in the calculator and trial division may differ but the result is always the same.

Prime Decomposition

Another popular method to find prime factorisation is known as prime decomposition and it includes the use of a factor tree. The factor tree diagram is an easy process to divide a number into its prime factors. To create a factor tree we have to break down the composite number into factors of the composite number till the numbers are prime.

There might be various methods to show the factor tree for any provided prime factorisation.

Here let’s take an example of 48 to check the prime factor using prime decomposition method.

Prime Factorisation of 48

It doesn’t matter whether you are using a calculator or find yourself, the factorisation will be unique always. And when there are very big numbers, the calculator is much more amazing!

Examples of Prime Decomposition: Factors and Exponents

  • Prime factorization of 100 is 2 x 2 x 5 x 5 or 22 x 52
  • Prime factorization of 76 is 2 x 2 x 19 or 22 x 191
  • Prime factorization of 50 is 2 x 5 x 5 or 2 x 52
  • Prime factorization of 48 is 2 x 2 x 2 x 2 x 3 or 24 x 31
  • Prime factorization of 36 is 2 x 2 x 3 x 3 or 22 x 32
  • Prime factorization of 20 is 2 x 2 x 5 or 22 x 51
  • Prime factorization of 10 is 2 x 5 or 21 x 51

Prime Factorisation Calculator is made by the team of lcmgcf.com to enhance your knowledge about the concepts and make it easier to understand the solution step by step.

Prime Factors Calcualtor Examples

FAQs on Prime Factorisation Calculator

Question 1: What is Prime Factorisation?

Answer 1: Prime factorisation means getting all the prime numbers that are factors of a number.

Question 2: What is The Sieve of Eratosthenes?

Answer 2: Eratosthenes invented a sieve to find prime numbers. It generally removes composite numbers and keeps prime numbers.

Question 3: What is a Composite Number?

Answer 3: When an integer number has more than two factors it is known as a composite number.

Question 4: Why find Prime Factors?

Answer 4: Prime Numbers can not be broken down so they are the basic blocks of all numbers. and this can be very helpful when working with large numbers, like in Cryptography.

Prime Factorisation Calculator