HCF (Highest Common Factor) - GCSE Maths Definition

The Highest Common Factor (HCF), also called the greatest common divisor, is the largest number that can exactly divide two or more numbers without leaving a remainder. To find the HCF of a set of numbers, you first list all the factors of each number, which are numbers they can be divided by, and then identify the biggest factor common to all the sets. For example, to find the HCF of 12 and 18, you would list the factors of 12 (1, 2, 3, 4, 6, 12) and 18 (1, 2, 3, 6, 9, 18), and notice that the largest number appearing in both lists is 6, making it the HCF. Understanding the HCF is useful when you want to simplify fractions or solve problems involving ratios.