Verified Solution • 2025–26 Session moderate

QJEEM22Ma5be5: JEE Main 2022 Mathematics - Class 11 JEEM22Ma5be5 Solution: The sum of all the elements of the set is __________.

The sum of all the elements of the set {α∈{1,2,.....,100}:HCF(α,24)=1}\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\} is __________.

Step-by-Step Verified Solution

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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