Highest Common Factor(H.C.F.) / Greatest Common Divisor (G.C.D.)

H.C.F of two or more numbers is the greatest number that can exactly divide each one of the number. It is also known as Greatest Common Divisor (G.C.D.).

Example:
       Consider the two numbers 4,16.
       The numbers that can divide 4 and 16 are 2,4.
       Here 4 is the highest number that can exactly divide both 4 and 16 , so 4 is the HCF of 4,16.

H.C.F can be calculated by any of the following methods:

Factorization Method:
Express each one of the numbers as product of prime factors.
The product of least powers of common prime factors gives HCF.

Example:
Greatest Common Measure of 36, 90, 72.

Step1: Express the numbers as product of prime factors.
        36 = 2² × 3²
        90 = 2 × 5 × 3²
        72 = 2³ × 3²

Step2: Take the prime numbers with least power and is present in all sets.
2 and 3 are the prime number common to all given numbers.

       The least power of 2 in the set is - 2
       The least power of 3 in the set is - 3²

Step3: Product of the numbers taken.
       3² × 2 = 9 × 2 = 18

       So 18 is the HCF/GCD.

Division Method:
Two find the HCF of two given numbers, divide the largest by the small number, then divide the dividend by the remainder. Repeat this until remainder is 0. The last dividend is the HCF of the two numbers.

Example: HCF of 27 & 36
       Step1: Divide 36/27 : remainder = 9

       Step2: Divide dividend by remainder
              27/9 : remainder = 0

       So the HCF /GCD of 27 and 36 is 9

For 3 numbers, calculate the HCF or greatest common measure(GCM) of 2 numbers, then HCF of the result with 3rd number. 

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Posted in: Division Method,Factorization Method,G.C.D,H.C.F,Numerical Operations