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Question

The sum of all the elements in the set {n{1,2,...,100}|H.C.F. of n and 2040 is 1} is equal to

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Solution

2040=233517
Let A= Sum of all numbers which are divisible by 2 upto 100.
B= Sum of all numbers which are divisilbe by 3 upto 100
C= Sum of all numbers which are divisible by 5 upto 100
D= Sum of all numbers which are divisilbe by 17 upto 100
ABCD=(A+B+C+D)(AB+AC+AD+BC+BD+CD)+(ABC+ABD+ACD+BCD)(ABCD)
=(50×51+33×51+1050+51×5)(51×16+550+102+315+51+85)+(180+0+0+0)0=3799
Required sum =50503799=1251

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