2025 Goals, Unlocked! Welcome 2025 with smarter learning. Discounts on all Plans! Make this your brightest year yet!
Exponential and Logarithmic Functions: Definition, Graphs, Properties, Examples
December 29, 2024
Application of Differential Equations: Definition, Types, Examples
December 29, 2024
Variations: Definition, Example, Types, Solved Questions
December 28, 2024
Algebraic Operations on Functions: Domain, Range, Formulas
December 28, 2024
Pascal’s Law – Formula, Application and Derivation
December 28, 2024
Comparing Fractions – Definition, Methods, Explanation, and Examples
December 28, 2024
Relationship Between LCM and HCF: Definition, Formulas, Solved Examples
December 28, 2024
Angles of Elevation and Depression: Definition Fact and Examples
December 28, 2024
Common Factors: Definition, Properties and Examples
December 27, 2024
Computation of Tax: Definition, Types, and Examples
December 27, 2024
Prime Factorisation: Prime factorisation is the process of breaking down a number into a set of prime numbers, which when multiplied back gives the original number. It is also called Integer Factorisation or Prime Decomposition.
Prime Factorisation is one of the important methods used to find the factors of a composite number. Prime Factorisation Method is also used to find the LCM & HCF of any given set of numbers. There are two Prime Factors Method through which we can easily find the factors of a number. In this article, we will provide you with all the necessary information on Prime Factorisation, its meaning, methods, and examples. Read on to find out more.
Prime Factorisation Defenition: For a given composite number, we will have to find the factors and these factors should be only prime numbers. When these Prime Numbers are multiplied back, it should give the actual number.
Prime Factorisation Algorithm
Before understanding the meaning of prime factorisation, let’s understand what is prime number and composite number.
| Composite Number | A number that has more than 2 factors is known as a Composite Number. Example: 4 = 1, 2, 4 (It can be divided by 1, itself and other numbers as well) |
| Prime Number | A number that has exactly 2 factors is known as a Prime Number. Example: 5 = 1, 5 (It can be divided by 1 and itself only) |
Note: 1 is not a Prime Number neither a Composite Number. Since 1 is the only factor of 1.
| Trigonometry Formulas | Algebra Formula |
| Mensuration Formulas | Differentiation Formulas |
| Factorisation Formulas | BODMAS Rules |
As explained above, prime numbers are the numbers which can be divided by the number itself and the number 1 only. The list of prime numbers from 1 to 100 are tabulated below:
| 2 | 17 | 41 | 67 |
| 3 | 19 | 43 | 71 |
| 5 | 23 | 47 | 73 |
| 7 | 29 | 53 | 79 |
| 11 | 31 | 59 | 83 |
| 13 | 37 | 61 | 89 & 97 |
Download the Prime Numbers Chart PDF from 1 to 10,000.
Also, Check:
| Maths Formulas For Class 11 | Maths Formulas For Class 12 |
| Maths Formulas For Class 10 | Maths Formulas For Class 9 |
| Maths Formulas For Class 8 | Maths Formulas For Class 6 |
Finding a prime factor of a number is similar to that of factoring a number. For example, we can find the Prime Factor of 20 as given below:
| Prime Factor of 20: 2, 2, 5 Prime Factor of 10: 2, 5 Prime Factor of 15: 3, 5 |
Finding prime factors for small numbers is easy. But, it is difficult to find the prime factors for large numbers such as 80, 145, etc.
There are 2 Prime Factorisation Methods through which we can find prime factors of large numbers.
As discussed above, there are 2 types of factorization methods and they are given below:
We can find the prime factors of a given composite number by dividing the number with the least prime number until the remainder is 1. The steps to solve the prime factorisation with the help of the division method are given below:
Prime Factorization Division Method Example
| Example: Calculate Prime Factors of 56 by Division Method 1st Step: Number 56 is divided by the least prime number 2. So, 56 ÷ 2. 2nd Step: Now the quotient is 28 and the remainder is 0. Divide 28 with the least prime number that is 2. So, 28 ÷ 2 3rd Step: 28 is divided by least prime number, i.e, 2. So the quotient is 14. So, 14 ÷ 2 4th Step: 14 is divided by least prime number and that is 2. The quotient is 7. 7 is a prime number as it cannot be divided by more than 2 factors. So 7 is the least prime number here. Prime Factors of 56 are 2 X 2 X 2 X 7. |
Let’s look at it in tabular format:
With the help of the Factor Tree Method, we can find prime factors of a given number. The Factor Tree Method steps are given below:
Prime Factorization Factor Tree Method Examples
Find the prime factorisation of 80 with the help of Factor Tree Method.
Q1. Find the prime factorization of 36?
A. Prime Factors of 36 are 2 X 2 X 3 X 3.
| Steps | Lowest prime factor with which the number is divisible | Quotient |
| 1st Step: 36 ÷ 2 | 2 | 18 |
| 2nd Step: 18 ÷ 2 | 2 | 9 |
| 3rd Step: 9 ÷ 3 | 3 | 3 (Cannot be broken down further as 3 is a Prime Number) |
Q2. Find the prime factorization of 24?
A. Prime Factors of 24 are 2 X 2 X 2 X 3.
| Steps | Lowest prime factor with which the number is divisible | Quotient |
| 1st Step: 24 ÷ 2 | 2 | 12 |
| 2nd Step: 12 ÷ 2 | 2 | 6 |
| 3rd Step: 6 ÷ 2 | 2 | 3 (Cannot be broken down further as 3 is a Prime Number) |
Q3. Find the prime factorization of 48?
A. Prime Factors of 48 are 2 X 2 X 2 X 2 X 3
| Steps | Lowest prime factor with which the number is divisible | Quotient |
| 1st Step: 48 ÷ 2 | 2 | 24 |
| 2nd Step: 24 ÷ 2 | 2 | 12 |
| 3rd Step: 12 ÷ 2 | 2 | 6 |
| 4th Step: 6 ÷ 2 | 2 | 3 |
Some frequently asked questions regarding prime factorization are given below:
A. i. Factorization is the process of finding factors which when multiplied back give the actual number. Factorization can be applied for both Prime Number and Composite Number.
ii. Prime Factorisation is the process of finding only Prime Factors of a given number. This can be applied only for Composite Number.
A. All the Prime Numbers are distinct numbers. 2 distinct Prime Factors are known as distinct Prime Numbers.
Example 1: Prime Factorization of 72: 2 X 2 X 2 X 3 X 3 (2 and 3 are distinct Prime Numbers)
Example 2: Prime Factorization of 330: 2 X 3 X 5 X 11 (2, 3, 5, 11 are 4 distinct Prime Numbers)
A. Prime factorization is the process of breaking down a number into a set of prime numbers, which when multiplied back gives the original number.
| Q1. Prime Factorization of 24. (Answer: 2 × 2 × 2 × 3) Q2. Prime Factorization of 48 (Answer: 2 × 2 × 2 × 2 × 3 ) Q3. Prime Factorization of 5005 (Answer: 5 × 7 × 11 × 13 ) Q4. Prime Factorization of 529 (Answer: 23 × 23 ) Q5. Prime Factorization of 120 (Answer: 2 × 2 × 2 × 3 × 5 ) Q6. Prime Factorization of 64 (Answer: 2 × 2 × 2 × 2 × 2 × 2 ) Q7. Prime Factorization of 729 (Answer: 3 × 3 × 3 × 3 × 3 × 3 ) |
Now you are provided with all the necessary information regarding Prime Factorisation. Students can make use of Embibe’s Mathematics Study page which covers almost all the Mathematical Concepts right from Grade 11 and Grade 12. All these concepts come with video lectures which can be accessed for.
Also, solve and take Maths Mock Tests on Embibe:
We hope this detailed article is helpful. If you have any queries regarding this article on Prime Factorization, please ping us through the comment box below and we will get back to you as soon as possible.
Scan to Download the App 
JEE Main