We will discuss here about the properties of HCF (highest common factor).

(i) The H.C.F. of two or more numbers cannot be greater than any one of them.

For example, the H.C.F. of 16, 18 and 24 is 2 which is less than all the given numbers.

(ii) If one number is a factor of the other numbers, their H.C.F. will be that smallest number.

For example, 8 is the H.C.F. of 8, 32 and 40.

(iii) The H.C.F. of the numbers is the product of the common prime factors.

For example, the H.C.F. of 14 and 28 is 14 which is the product of the common prime factors 2 and 7

(Since 1 is always a common factor of all numbers, so usually we do not write 1 as common factor. It is understood.)

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