HCF (Highest Common Factor),

The greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor. It is also called the Greatest Common Measure(GCM) and Greatest Common Divisor(GCD). HCM and LCM are two different methods, whereas LCM or Least Common Multiple is used to find the smallest common multiple of any two or more numbers.

Example: The Highest common factor of 60 and 75 is 15 because 15 is the largest number which can divide both 60 and 75 exactly.

We can find the HCF of any given numbers by using two methods:

• by prime factorization method

• by division method

  HCF By Prime Factorization Method

  Follow the below-given steps to find the hcf of numbers using prime factorization method.
  Step 1: Write each number as a product of its prime factors. This method is called here prime factorization.
  Step 2: Now list the common factors of both the numbers
  Step 3: The product of all common prime factors is the HCF( use the lower power of each common factor)
  Let us understand with the help of examples.
  Example 1: Evaluate the HCF of 60 and 75.
  Solution:

  Write each number as a product of its prime factors. 22 x 3 x 5 = 60 3 x 52 = 75 The product of all common prime factors is the HCF( use the lowes power of each common factor) The common prime factors in this example are 3 & 5. The lowest power of 3 is 3 and 5 is 5. So, HCF = 3 x 5 = 15

  Example 2: Find the HCF of 36, 24 and 12.
  Solution:

  Write each number as a product of its prime factors. 22 x 32 = 36 23 x 3 = 24 22 x 3 = 12 The product of all common prime factors is the HCF( use the lowes power of each common factor) The common prime factors in this example are 2 & 3. The lowest power of 2 is 22 and 3 is 3. So, HCF = 22 x 3 = 12

  Example 3: Find the HCF of 36, 27 and 80.
  Solution:

  Write each number as a product of its prime factors. 22 x 32 = 36 33 = 27 24 x 5 = 80 The product of all common prime factors is the HCF( use the lowes power of each common factor) The common prime factors in this example are none. So, HCF is 1.

  HCF By Division Method

  You have understood by now the method of finding the highest common factor using prime factorization. Now let us learn here to find HCF using division method. Basically division method is nothing but dividing the given numbers simultaneously to get the common factors between them. Follow the steps mentioned below to solve problems of hcf.
  • Step 1: Write the given numbers horizontally, in a sequence, by separating it with commas.
  • Step 2: Find the smallest prime number which can divide the given number. It should exactly divide the given numbers. (Write in the left side).
  • Step 3: Now write the quotients.
  • Step 4: Repeat the process, until you reach the stage, where there is no coprime number left.
  • Step 5: We will get the common prime factors as the factors in the left-hand side divides all the numbers exactly. The product of these common prime factors is the HCF of the given numbers.
  Let us understand the above-mentioned steps to find the HCF by division method with the help of examples.
  Problem 1: Evaluate the HCF of 30 and 75
  
  As we can note that the mentioned prime factors in the left side divide all the numbers exactly and so, they all are common prime factors. We have no common prime factor for the numbers remained at the bottom.
  So, HCF = 3 × 5 = 15.
  Example 2: Find out HCF of 36, and 24
  
  HCF = 2 × 2 × 3 = 12.
  Example 3: Find out HCF of 36, 12, 24 and 48.
  
  HCF = 2 × 2 × 3 = 12.

  HCF by Shortcut method

  Steps to find the HCF of any given numbers.
  • Step 1: Divide larger number by smaller number first, such as;
  Larger Number/Smaller Number
  • Step 2: Divide the divisor of step 1 by the remainder left.
  Divisor of step 1/Remainder
  • Step 3: Again divide the divisor of step 2 by the remainder.
  Divisor of step 2/Remainder
  • Step 4: Repeat the process until the remainder is zero.
  • Step 5: The divisor of the last step is the HCF.