The sum of two numbers is 2604 and their HCF is 124. Which is the smaller between them if their difference is the least possible?

To solve this problem, we need to understand that the difference between two numbers is least when they are as close to each other as possible.

Given that the highest common factor (HCF) is 124, we know that both numbers are multiples of 124.

Let's denote the two numbers as 124a and 124b, where a and b are integers.

We know that 124a + 124b = 2604, which simplifies to a + b = 21 (after dividing the whole equation by 124).

Since a and b are integers and we want the difference between the two numbers to be as small as possible, the best way to divide 21 into two parts is to make a and b as close as possible.

The two numbers that fit this condition are 10 and 11.

So, the two numbers are 12410 = 1240 and 12411 = 1364.

Therefore, the smaller number is 1240.