HCF is the abbreviation for Highest Common Factor. The term HCF or Highest Common Factor denotes the greatest among the given set of two or more two numbers.
The methods of division and prime factorization are the two methods that are used to find the solutions pertaining to the Highest Common Factor (HCF) and Lowest Common Factor (LCM). The easiest and the most convenient and also the method that utilizes a lesser amount of time to find the solution for HCF is the division method. Even the method is convenient and less time-consuming to find the solution for the problems pertaining to Least Common Factor or LCM.
The basic rules of mathematics state that the GCD or the greatest common Divisor of the two or more integers that are positive in nature is always the integer that is the largest (and also positive in nature). This number divides the number such that there remains no remainder.
Let us consider the numbers 8 and 12. Here when we consider solving it by the method of division then we will find the Highest Common Factor or the HCF of the two given numbers 8 and 12 to be 4. The Highest Common Factor or the HCF of the two given numbers 8 and 12 happens to be 4 because it is the digit 4 that divides the numbers 8 and 12 without leaving any integer behind.
Formula to find the Highest Common Factor or the HCF of any given integer:
The product of two given integers = (the HCF of 2 numbers) * (the LCM of 2 numbers)