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

JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Permutations and Combinations

The sum of all the elements in the set

{n \in {1, 2, \dots, 100} ∣

H.C.F. of

n

and 2040 is 1

}

is equal to ____

Answer: 1251

Since

2040 = 2^{3} \times 3 \times 5 \times 17

, the elements counted are those divisible by none of

2

3

5

and

17

. Striking the even numbers, the multiples of

3

, of

5

and of

17

out of

1

100

leaves

1, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97

These

25

numbers add up to

1251

JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Integer answer