Highest Common Factor (HCF) Mean in Math

The Highest Common Factor (HCF) of two numbers is the greatest possible number that divides both the numbers completely. The Highest Common Factor (HCF) is also said the Greatest Common Divisor (GCD).

There are many ways to calculate the HCF of two numbers. One of the quickest ways to calculate the HCF of two or more numbers is by using the prime factorization method. Explore the world of HCF by going through its different aspects and properties.

Calculate answers to questions like what is the greatest common factor for a group of numbers, easy ways to find HCF, HCF by division method, its relation with LCM, and discover more interesting facts around them.

Definition of HCF

The HCF (Highest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. in simple words, the highest common factor(HCF) of two natural numbers x and y is the largest possible number that divides both x and y.

Let us learn this definition using two numbers, 16 and 24. The common factors of 16 and 24 are 1, 2, 4and 8. Among these numbers, 8 is the highest number. So, the HCF of 16 and 24 is 8. This is written as: HCF (16, 24) = 8. Observe the following figure to understand this concept.

How to Find HCF?

There are many methods to calculate the highest common factor of the given numbers. For every method, the result to the HCF of the numbers would always be the same. There are 3 methods to find the HCF of two numbers:

• HCF by listing factors method
• HCF by prime factorization
• HCF by division method

Properties of HCF

We already know that the HCF of a and b is the highest common factor of the numbers a and b. Let us have a look at the important properties of HCF:

The properties of the highest Common Factor are given below.

• The highest common factor of two or more numbers divides each of the numbers without a remainder.
• The highest common factor of two or more numbers is a factor of each of the numbers.
• The highest common factor of two or more numbers is always less than or equal to each of the numbers.
• The highest common factor of two or more prime numbers is 1 always.