Prime Factorisation Calculator

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.

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.

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.

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.

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.

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.

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.