Class 5 - Prime Factorisation: Definition, Methods, Solved Examples

Understanding prime factorization is important for solving mathematical problems based on HCF and LCM. To understand prime factorisation it is important to understand prime numbers. A prime number is a number that has exactly two factors: 1 and itself. If a factor of a number is a prime number, then it is called a prime factor of the number. Prime factorization is a way of representing a number as its prime factors. Let’s learn more about prime factorisation methods with examples below.

Table of Contents

• What is Prime Factorization
• Prime Factorization Method
• Solved Examples on Prime Factorization

What is Prime Factorization

Prime factorisation is a method of representation of a number as a product of its prime factors 

It helps us in breaking down a number into a product of its prime numbers. For example, the prime factorization of 24 is 2 × 2 × 2 × 3, which can also be written as 2³ × 3. 

In simple words, if we decompose a number until we can no longer break it down except by using prime numbers, we get the prime factorization of that number.

 

Prime Factorization Method

Factor-Tree Method:

A factor tree is a diagram used to determine the prime factors of any number greater than 1.

Step 1: Find a pair of factors whose product is the given number and write them below the number.

Step 2: If one of the two factors is prime, keep it unchanged and repeat Step 1 for the composite

number. In case both the factors are composite numbers, then follow Step 1 for both the factors.

Step 3: Continue the process till you get all the factors as prime numbers.

For example: Prime factorisation of 36. The prime factors of 36 are 2 × 2 × 3 × 3.

 

Division Method:

Step 1: Divide the given number by one of its prime factors and write the quotient below the number.

Step 2: Repeat Step 1 for the quotient obtained.

Step 3: Continue this process until you get 1 as the quotient.

Example 2: Show the prime factorisation of 36.

 

Solved Examples on Prime Factorization

Example 1: Prime Factorization of 50 
Solution:
Step 1: Divide 50 by the least prime number, which is 2.
50 ÷ 2 = 25

Step 2: Divide 25 by the next smallest prime number, 5.
25 ÷ 5 = 5

Step 3: Divide 5 by 5.
5 ÷ 5 = 1

As we have reached 1, we stop.

So, the prime factorization of 50 is 2 × 5 × 5, or in exponential form: 2 × 5².

 

Example 2: Prime Factorization of 60.
Solution:
Step 1: Divide 60 by the least prime number, which is 2.
60 ÷ 2 = 30

Step 2: Divide 30 by 2 again.
30 ÷ 2 = 15

Step 3: Divide 15 by the next prime number, 3.
15 ÷ 3 = 5

Step 4: Divide 5 by 5.
5 ÷ 5 = 1

As we have reached 1, we stop.

So, the prime factorization of 60 is 2 × 2 × 3 × 5, or in exponential form: 2² × 3 × 5

Example 3: Prime Factorization of 15.
Solution:
Step 1: Divide 15 by the least prime number, which is 3.
15 ÷ 3 = 5

Step 2: Divide 5 by 5 again.
5 ÷ 5 = 1

As we have reached 1, we stop.

So, the prime factorization of 15 is 3 × 5 x 1.