If for integer a, b and c if HCF(a,b) = 1 and HCF(a,c) = 1

If for integer a, b and c if HCF(a,b) = 1 and HCF(a,c) = 1, then which one of the following is correct?

  1. HCF(a,bc) = a
  2. HCF(a,bc) = b
  3. HCF(a,bc) = 1
  4. None

Answer

If HCF(a,b) = 1 and HCF(a,c) = 1, then HCF(a,bc) = 1

For example, take a = 2, b = 3 and c = 5

HCF(2,3) = 1

HCF(2,5) = 1

and HCF(2,15) = 1

The correct option is C.