JEE MAIN - Mathematics (2022 - 24th June Evening Shift - No. 19)
The sum of all the elements of the set $$\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\} $$ is __________.
Answer
1633
Explanation
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 = 96
There are four such blocks and a number 97 is there upto 100.
$$\therefore$$ Complete sum
= 96 + (24 $$\times$$ 8 + 96) + (48 $$\times$$ 8 + 96) + (72 $$\times$$ 8 + 96) + 97
= 1633
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