The sum of all the elements of the set ∈ 1, 2,..., 100 : HCF ( , 24) = 1 is_____.

Question

Accepted Answer

Correct answer: 1633. (1633) HCF ( , 24) = 1 Now, 24 = 22.3 is not the multiple of 2 or 3 Sum of values of = S(U) -S(multiple of 2) + S (multiple of 3) - S(multiple of 6) = (1 + 2 + 3 +......100) - (2 + 4 + 6.....+ 100) - (3 + 6 +.....99)+ (6+12+.....+96) = 100 1012-50 51- 332 (3+99)+ 162(6+96) = 5050 - 2550 - 1683 + 816 = 1633 Ans.

$The sum of all the elements of the set { {1, 2,..., 100} : HCF (, 24) = 1} is_____.$

Solution

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