Question

The sum of all the elements of the set {α ∈ {1, 2, …, 100} : HCF(α, 24) = 1} is

Answer 1

The correct answer is 1633
The numbers upto 24 which gives g.c.d. with 24 equals to 1 are 1, 5, 7, 11, 13, 17, 19 and 23.
Sum of these numbers is 96
There are four such blocks and a number 97 is there upto 100.
∴ Complete sum
= 96 + (24 × 8 + 96) + (48 × 8 + 96) + (72 × 8 + 96) + 97
= 1633