JEE MAIN - Mathematics (2021 - 22th July Evening Shift - No. 19)
The sum of all the elements in the set {n$$\in$$ {1, 2, ....., 100} | H.C.F. of n and 2040 is 1} is equal to _____________.
Answer
1251
Explanation
2040 = 23 $$\times$$ 3 $$\times$$ 5 $$\times$$ 17
n should not be multiple of 2, 3, 5 and 17.
Sum of all n = (1 + 3 + 5 + ...... + 99) $$-$$ (3 + 9 + 15 + 21 + ...... + 99) $$-$$ (5 + 25 + 35 + 55 + 65 + 85 + 95) $$-$$ (17)
= 2500 $$-$$ $${{17} \over 2}$$(3 + 99) $$-$$ 365 $$-$$ 17
2500 $$-$$ 867 $$-$$ 365 $$-$$ 17
= 1251
n should not be multiple of 2, 3, 5 and 17.
Sum of all n = (1 + 3 + 5 + ...... + 99) $$-$$ (3 + 9 + 15 + 21 + ...... + 99) $$-$$ (5 + 25 + 35 + 55 + 65 + 85 + 95) $$-$$ (17)
= 2500 $$-$$ $${{17} \over 2}$$(3 + 99) $$-$$ 365 $$-$$ 17
2500 $$-$$ 867 $$-$$ 365 $$-$$ 17
= 1251
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