Logic of HCF or GCD of any two numbers: In HCF we try to find any largest number which can divide both the number. For example: HCF or GCD of 20 and 30 Both number 20 and 30 are divisible by 1, 2,5,10. HCF=max (1, 2, 3, 4, 10) =10 Logic for writing program: It is clear that any number is not divisible by greater than number itself. In case of more than one numbers, a possible maximum number which can divide all of the numbers must be minimum of all of that numbers. For example: 10, 20, and 30 Min (10, 20, 30) =10 can divide all there numbers. So we will take one for loop which will start form min of the numbers and will stop the loop when it became one, since all numbers are divisible by one. Inside for loop we will write one if conditions which will check divisibility of both the numbers. Program: