HCF Questions with Answers (Solved Examples & Practice for Class 5–7)

HCF questions are an important part of mathematics, especially for school exams and Olympiads. Learning to find the Highest Common Factor (HCF) helps in solving everyday problems involving equal distribution and arranging items into groups. On this page, you will learn different methods to solve HCF questions and HCF problems, along with step-by-step examples and practice questions.

Table of Contents

• What is HCF?
• How to Calculate the HCF?
• Sample HCF Questions
• Practice Questions on HCF Questions
• Applications of HCF Concepts
• Frequently Asked Questions on HCF Questions & Answers

What is HCF?

HCF (Highest Common Factor) is the largest number that divides two or more numbers exactly. It is also called the Greatest Common Divisor (GCD).

Example: Find the HCF of 12 and 18.

Solution:
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 18 = 1, 2, 3, 6, 9, 18

Common factors = 1, 2, 3, 6
Highest common factor = 6

Answer: 6

How to Calculate the HCF?

To solve HCF questions and find the HCF easily, we can apply different methods of calculation. Below are the three most commonly used methods.

The above-stated methods of finding HCF will make it easy for you to solve all types of HCF questions, whether small or large numbers.

Method 1: Prime Factorisation Method (Learn more on Prime Factorization)

Steps:

1. Find prime factors of each number
2. Take common factors
3. Multiply them

Example: Find HCF of 18 and 24

18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3

Common factors = 2 × 3 = 6

Method 2: Division Method

Steps:

1. Divide larger number by smaller
2. Divide divisor by remainder
3. Repeat until remainder = 0

Example: Find HCF of 16 and 12

16 ÷ 12 = remainder 4
12 ÷ 4 = remainder 0

HCF = 4

Method 3: Listing Method

Example: Find the HCF of 20 and 30 using the listing method.

Solution:

Step 1: List the factors of 20
1, 2, 4, 5, 10, 20

Step 2: List the factors of 30
1, 2, 3, 5, 6, 10, 15, 30

Step 3: Identify the common factors
1, 2, 5, 10

Step 4: Choose the highest common factor
HCF = 10

Read more:

• HCF and LCM Questions
• HCF and LCM
• LCM Questions

Solved HCF Questions

Let’s understand how to find HCF through some solved HCF examples.

Example 1: What is the HCF of 24 and 36?

Solution:

First, list the factors of 24, i.e., 1, 2, 3, 4, 6, 8, 12, 24

List the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Identify the highest common factor: 12

HCF = 12

Example 2: Find the HCF of 135 and 225 using prime factorisation.

Solution:

First, let’s find the prime factors of 135, i.e., 3 × 3 × 3 × 5

Now, find the prime factors of 225, i.e., 3 × 3 × 5 × 5

The common prime factors are 3 × 3 × 5 = 45

Final Answer: HCF = 45

Example 3: What is the highest common factor of 96 and 404?

Solution:

Write the prime factors of 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3

Write the prime factors of 404 = 2 × 2 × 101 = 2² × 101

HCF(96, 404) = 2 x 2 = 4

Example 4: If the HCF of two numbers is 29 and their sum is 174, what will be the value of the numbers?

Solution:

Given that the HCF of two numbers is 29.

Let 29a and 29b be the two required numbers.

According to the given,

29a + 29b = 174

29(a + b) = 174

a + b = 174/29 = 6

The pair of coprime values with sum 6 is (1, 5).

So, the possible numbers are 29 x 1 = 29

29 x 5 = 145

Verification:

Sum of numbers = 29 + 145 = 174

Hence, the required numbers are 29 and 145.

Example 5: Find the highest common factor of the fractions 2/3 & 5/8.

Solution:

Formula to find the HCF of Fractions = HCF of numerator / LCM of denominator

For the given fractions, 2/3 & 5/8, the numerators are 2 & 5, while the denominators are 3 & 8.

The first step is to find the HCF of the numerator (2, 5) = 1

LCM of the denominator (3, 8) = 24

Therefore, the HCF of 2/3 and 5/8 is 1/24.

Example 6: There are two wires of length 30 cm and 60 cm. If the wire is to be cut into equal pieces, what will be the length of each piece?

Solution: HCF of 30 and 60.

30 = 2 × 3 × 5

60 = 2 × 2 × 3 × 5

Common factors: 2 × 3 × 5 = 30

HCF = 30, so the length of each piece = 30 cm

Example 7: Find the HCF of 16 and 12 using the division method.

Solution: To find the HCF of 16 and 12, divide the larger number by the smaller number.

16 ÷ 12 = 1, remainder = 4

Now divide the previous divisor by the remainder:

12 ÷ 4 = 3, remainder = 0

Since the remainder is now 0, the last divisor is the HCF.

HCF = 4

Practice Questions on HCF Questions

Try the following practice questions to test your understanding of HCF concepts.

1. Find the HCF of 24 and 36.

2. The HCF of 18 and 27 is ______.

3. What is the HCF of 20 and 28?
a) 2
b) 4
c) 7
d) 10

4. True or False: The HCF of 16 and 24 is 8. ______

5. 36 pencils and 48 pens are to be packed into equal boxes so that each box has the same number of pencils and pens. What is the maximum number of boxes?

6. Two ribbons are 45 cm and 60 cm long. They are cut into equal pieces of maximum length. What is the length of each piece?

7. Find the Missing Number: HCF of 12 and ___ is 6. Write any one possible number.

8. Assertion: HCF of 9 and 15 is 3.
Reason: 3 is the greatest number that divides both 9 and 15.
a) Both are true
b) Both are false
c) Assertion is true, reason is false
d) Assertion is false, reason is true

9. Find the HCF of 12, 18, and 30.

10. Two numbers have HCF 5. One number is 25. Write any one possible value of the second number.

Applications of HCF Concepts

The concept of HCF questions is used in various fields such as packaging, dividing things evenly, designing timetables, or even in banking systems. Learning these skills will help you to apply math far beyond exams. Practising the HCF questions with our worksheets will not only help you gain an in-depth understanding of the concepts but will also enable you to build a solid foundation for high-level competitive exams.

 

Frequently Asked Questions on HCF Questions & Answers

1. What is HCF?

Answer: The highest common factor of a given set of numbers is defined as the highest number that can divide each number in the set.

2. What are the various methods used to find the HCF?

Answer: Prime factorisation, division and listing method are some of the methods used to find the HCF.

3. List the steps to calculate the HCF of three numbers.

Answer: The step-by-step process to find the HCF of three numbers is listed below:

• Calculate the HCF of the first two numbers given in the question.
• Then, calculate the HCF of the third number and the answer derived from the above step.
• The HCF of the given three numbers is the number obtained from step 2.

Example: Find the HCF of 12, 18, and 24.

Solution:
Step 1: HCF of 12 and 18 = 6
Step 2: HCF of 6 and 24 = 6

Final Answer: HCF = 6

4. What is the difference between HCF and LCM?

Answer: HCF is the greatest number that divides given numbers exactly, while LCM is the smallest number that is a multiple of the given numbers.