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The sum of all the elements of the set {α ∈ {1, 2, ..., 100} : HCF(α, 24) = 1} is ____. (In integers)
Correct answer is '1633'. Can you explain this answer?
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The sum of all the elements of the set {α ∈ {1, 2, ..., 100...
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The sum of all the elements of the set {α ∈ {1, 2, ..., 100...
HCF(α, 24) = 1
Now, 24 = 23.3
→ α is not the multiple of 2 or 3.
Sum of values of α = 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)
= 5050 - 2550 - 1683 + 816 = 1633
Now, 24 = 23.3
→ α is not the multiple of 2 or 3.
Sum of values of α = 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)
= 5050 - 2550 - 1683 + 816 = 1633
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The sum of all the elements of the set {α ∈ {1, 2, ..., 100} : HCF(α, 24) = 1} is ____. (In integers)Correct answer is '1633'. Can you explain this answer?
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