What is the highest common factor (HCF)?
The highest common factor (HCF) of two or more numbers is the largest number which you can divide all your starting numbers by and get whole number answers. How is it calculated? You start by splitting your numbers into their prime factors. If you then pick out all the prime factors that are common to both numbers and multiply them together, you will get the HCF. For example, 924 = 2^2 x 3 x 7 x 11 and 3080 = 2^3 x 5 x 7 x 11. The factors these numbers have in common are 2^2, 7 and 11. Therefore the HCF is given by 2^2 x 7 x 11 = 308. Why is the HCF useful? Knowing the HCF of two numbers is useful, for example, when trying to cancel down fractions. For example, if you had the fraction 924/3080, you can divide both the numerator and denominator by the HCF (which is 308, as calculated above) to get the more tidy looking 3/10. What is the least common multiple (LCM)? The least common multiple (LCM) of two or more numbers is the lowest number of which your starting numbers are all factors.
