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Practice Finding HCF (GCD)

Worksheet Description

Practice finding HCF (GCD) with interactive worksheets. Solve 2 to 5 number problems, choose difficulty, and get instant feedback online.

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Introduction

This worksheet provides interactive practice for finding the Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), of two or more integers. It helps learners develop strong factorization skills through structured, self-correcting problems.

What Is HCF (GCD)

The Highest Common Factor (HCF) of two or more numbers is the greatest number that divides all of them exactly without leaving a remainder.

For example, the HCF of 12 and 18 is 6, because 6 is the largest number that divides both numbers completely.

The HCF (GCD) of two or more integers is always less than or equal to the smallest number in the set.

Worksheet Features

This is an online, interactive, and self-correcting worksheet where learners enter answers directly in the browser.

  • Generate 8, 16, or 24 problems per worksheet
  • Each problem includes 2 to 5 integers
  • Instant feedback for every answer
  • No printing or downloading required

Configurable Practice Options

Learners can customize the worksheet based on their level and preference.

  • Number Count: Choose 2, 3, 4, or 5 integers per problem.
  • Difficulty Levels: Easy, Medium, or Hard.

Two Standard Methods to find HCF

1. Prime Factorization Method

  • Factor each number into Primes
  • Identify the common Prime factors
  • Take the lowest power of each common Prime
  • Multiply them together

2. Division (Ladder) Method

  • Write all numbers in a row
  • Divide them by a common Prime number
  • Repeat until no further common division is possible
  • Multiply the divisors

Let's understand both these methods using the below examples.

Finding HCF using Prime Factorization Method

In the Prime Factorization method, each number is expressed as a product of its prime factors. The HCF is obtained by multiplying together all those prime factors that are commonly present in all the given numbers.

24, 36, 60, 96 and 120

 

The Prime Factors

24
2
2
2
3
36
2
2
3
3
60
2
2
3
5
96
2
2
2
2
2
3
120
2
2
2
3
5

Presenting in tabular format grouped by the distinct Prime factors 2, 3, 5.

2
3
5
24
2
2
2
3
36
2
2
3
3
60
2
2
3
5
96
2
2
2
2
2
3
120
2
2
2
3
5

Take only the Prime factors common to all the numbers, using the lowest power of each.

2, 2 and 3

The HCF is the product of all these common Prime Factors.

The HCF(24, 36, 60, 96, 120) is:

=223

=12

Finding HCF using Division Method

The Division (Ladder) method is a systematic way to find the HCF by dividing the numbers by common prime factors.

24, 36, 60, 96 and 120

224366096120
21218304860
369152430
235810

Divide the numbers by Prime numbers as long as all those numbers are divisible by that prime number.

When there is no common Prime factor across all numbers at a particular step, the Division (Ladder) method stops at that step.

The HCF (GCD) is the product of all the Prime Numbers in the 1st column of the above table.

The HCF(24, 36, 60, 96, 120) is:

=223

=12

How to Work Through the Problems

For each problem, find the HCF of the given integers using any method you prefer.

Enter the final answer directly into the input box. No intermediate steps are required.

View Step-by-Step Solutions

Each problem includes a Solution link that opens an interactive online tool, Highest Common Factor (HCF) Calculator, showing the full step-by-step working for that specific problem.

You can also use the same tool independently by entering your own inputs directly. This lets you explore new problems, verify answers, and understand the method in detail — all in one place.

Use the Solution link for guided help, or go to the tool and try your own examples.

Online, Interactive, and Self-Correcting

This worksheet runs entirely in the browser.

As you enter answers, the system checks them instantly, helping you correct mistakes and build confidence quickly.

Click on the green box in the first problem of the worksheet to get started!!