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 __________.

Step-by-step solution

The prime factorisation of the given number is 2040 = 2 3 × 3 × 5 × 17 The H.C.F. of n and 2040 is 1 if n is not a multiple of 2 ,   3 ,   5 and 17 . Hence n cannot be multiple of 2 , 3 , 5 and 17 Then sum is n ( 1 ) - ( n ( 2 ) + n ( 3 ) + n ( 5 ) + n ( 17 ) - n ( 6 ) - n ( 10 ) - n ( 34 ) - n ( 15 ) - n ( 51 ) - n ( 85 ) ) + n ( 30 ) ) Where n ( a ) means the sum of all numbers belonging to the set 1 , 2 , … … . 100 which are divisible by a = 100 × 101 2 - 2 × 50 &#2