Highest Common Factor

The Highest Common Factor (HCF) of two or more numbers is the greatest of all their common factors. Therefore, it is also called the greatest common factor (GCF). If we say M is the highest common factor of N, then M is the highest possible number that divides the number N.

For example, the common factors of 12 and 16 are 1, 2 and 4. But the highest common factor of 12 and 16 will be 4, which is common to both the numbers.

In this article, we will learn to find the HCF of two or more numbers along with examples in simple ways. Class 6 students will be able to excel in the concept of highest common factor by reading this article.

Learn more: HCF

How to Find the Highest Common Factor?

The highest common factor (HCF) is easy to evaluate by just listing the factors of the given numbers and then picking the largest of all the common factors. We can list down all the factors using the prime factorisation method. So follow the below steps to find HCF:

  • Find the prime factors of using factorisation of each number
  • Write the numbers in their respective product form of prime factors
  • Now, find the common prime factors among the following numbers
  • The HCF of the given numbers will be the product of common prime factors

Also, check: HCF of Two Numbers

Facts:

  • HCF of two consecutive integers is 1
  • HCF of two consecutive even integers is 1
  • HCF of two consecutive odd integers is 1
  • HCF of two co-primes is equal to 1

Solved Examples

Q.1: Find the HCF of the following numbers:

(a) 30, 104

(b) 15, 25, 72

Solution:

(a) 30, 104

By prime factorisation of 30 and 104, we get;

Factors of 30 → 1, 2, 3, 5, 6, 10, 15, 30

Factors of 104 → 1, 2, 4, 8, 13, 26, 52, 104

As we can see, among all the factors, 2 is the only highest common factor for 30 and 104.

Therefore, HCF (30, 104) = 2

(b) 15, 25, 75

By prime factorisation of 15, 25 and 75, we get;

Factors of 15 → 1, 3, 5, 15

Factors of 25 → 1, 5, 25

Factors of 75 → 1, 3, 5, 15, 25, 75

Therefore, HCF of (15, 25, 75) = 5

Q.2: What is the GCF of 10, 50 and 100?

Solution: By prime factorisation, we can list the prime factors of 10, 50 and 100, respectively.

Factors of 10 → 1, 2, 5, 10

Factors of 50 → 1, 2, 5, 10, 25, 50

Factors of 100 → 1, 2, 4, 5, 10, 20, 25, 50, 100

Therefore, the HCF of (10, 50, 100) = 10.

Practice Questions

  1. Find the HCF of 20, 62.
  2. Find the GCF of 91, 112, 49.
  3. What is the highest common factor of the following numbers?
    1. 34, 36, 40
    2. 88, 99
    3. 12, 15, 21
    4. 50, 60, 70

Frequently Asked Questions on Highest Common Factor

What is the highest common factor?

The Highest Common Factor (HCF) of two or more numbers is the greatest possible number of all their common factors.

What is the highest common factor of 8 and 12?

The highest common factor of 8 and 12 is 4.

What is the H.C.F. of 45 and 60?

The H.C.F. of 45 and 60 is 15.

What is the HCF of two consecutive numbers?

The HCF of any two consecutive numbers will always be 1. Since, the difference between the two consecutive numbers is 1. For example, HCF of 3 and 4 is 1.

What is the GCF of 42 and 162?

The greatest common factor of 42 and 162 is 6.

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