The highest (or largest) common factor of two or more given integers is called the Highest Common Factor (H.C.F.). Additionally, it is referred to as the Greatest Common Divisor (GCD) or the Greatest Common Measure ( GCM )

In other terms, the highest common factor of two or more integers is the biggest number that precisely divtopicIdes all the provtopicIded numbers.

There are two frequently used techniques for determining the H.C.F. of multiple numbers:

1)Method of Prime Factorization

2)Method of Continual Division

METHOD 1: Method of Prime Factorization

To determine the H.C.F. of two or more integers, the following method may be used:

STEP 1) Check out the numbers. Assume the integers 12 and 20.

STEP 2) Calculate the prime factors of the given numbers.

20 = 20 x 1;

20 = 4 x 5;

20 = 10 x 2;

Or 

For the number 20:

20/2 = 10; 10/2 = 5; 5/5 = 1.

Therefore, factors of 20 are 2, 2, 5.

12 = 12 x 1

12 = 4 x 3

12 = 6 x 2

OR

For the number 12:

12/2 = 6; 6/3 = 2; 2/2 = 1.

Therefore, factors of 12 are 2, 2, 3.

STEP 3) Determine the presence of common prime factors.

In the cases of 12 and 20, the most often occurring prime factors are 2 and 2.

STEP 4) Determine the minimal number of times each common prime factor appears in the prime factorizations of the supplied integers.

For instance, the prime factor 2 occurs exactly once in the prime factorization of 20, whereas the prime factor 2 appears exactly once in the prime factorization of 12.

STEP 5) Multiply each common prime component by the specified number of times and find their product to get the necessary H.C.F.

Thus, the H.C.F. of 12 and 20 is equal to 2 x 2 = 4.

METHOD 2: Method of Common Factorization 

STEP 1) Obtain the two numbers and determine which is the greater.

STEP 2) DivtopicIde the largest number by the smallest.

STEP 3) Determine the product's quotient. This will be your factor.

STEP 4) Keep divtopicIding and finding factors until the remainder is zero. Otherwise, go to the subsequent step.

STEP 5) List down the common factors of the two numbers.

Step 6) H.C.F will be the greatest common number between the two numbers. This can be extended to three or more numbers.

Let us constopicIder the same numbers 12 and 20.

OR

Find the multiples of both numbers 12 and 20.

Multiples of the number 20: 

20 = 20 x 1;

20 = 4 x 5;

20 = 10 x 2;

Therefore, factors of 20 are 1, 2, 4, 5, 10, 20.

Multiples of the number 12:

12 = 12 x 1

12 = 4 x 3

12 = 6 x 2.

Therefore, factors of 12 are 1, 2, 3, 4, 6, 12.

The common factors of 12 and 20 are 1, 2, 4.

Among 1, 2, and 4, the greatest common factor is 4.

Therefore, the Highest common factor is 4 for the numbers 12 and 20.