The HCF and LCM of two numbers are 8 and 21600 respectively. Given that one of the numbers is 200, find the other possible number.
The relationship between the highest common factor (HCF) and the least common multiple (LCM) of two numbers (let's call them A and B) can be represented by the following equation:
A * B = HCF(A, B) * LCM(A, B)
In this case, you're looking to find one of the numbers, given that the other number is 200, and the HCF and LCM are 8 and 21600, respectively. We can plug these values into the equation to find the other number.
Let A = 200 (the given number)
Let B = x (the number we want to find)
The equation becomes:
200 * x = 8 * 21600
Now we solve for x:
x = (8 * 21600) / 200
x = (8 * 108) // because 21600 / 200 = 108
x = 864
So, the other number is 864. The two numbers are 200 and 864, with an HCF of 8 and an LCM of 21600.