HCF & LCM of Numbers

Highest Common Factor

Highest Common Factor: The HCF of two or more than two numbers is the greatest number that divides each of them exactly.

There or two methods to find the HCF

                  1. Factorization Method

                  2. Division Method

Factorization Method

Express each one of the given numbers as the product of prime factors The product of least powers of common prime factors gives HCF

Example: 

       Find the HCF of 108,288 and 360.

       Answer:  \(108=2^{2} \times 3^{3}\)

                       \(288=2^{5} \times 3^{2}\)

                      \(360=2^{3} \times 5 \times 3^{2}\)     

                   HCF =  \(2^{2} \times 3^{2}=36\)

                       

Division Method

Suppose we have to find the H.CF. of two given numbers. Divide the larger number by the smaller one. Now, divide the divisor by the remainder. Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder. The last divisor is the required HCF

Finding the H.C.F. of more than two numbers: Suppose we have to find the H.C.F. of three numbers. Then, H.C.F. of  [ H.C.F.(HCF(any two) and (the third number))]  gives the H.C.F. of three given numbers.

Similarly, the H.C.F. of more than three numbers may be obtained.