Let-N-be-a-natural-number-where-N-100-If-HCF-N-100-1-then-find-the-sum-of-all-the-values-of-N-a-400-b-1000-c-2000-d-4000-

Question Number 194528 by BaliramKumar last updated on 09/Jul/23

★ Let N be a natural number where N \leq 100 .

If HCF (N, 100) = 1 then find the sum of

all the values of N ?

(a) 400 (b) 1000 (c) 2000 (d) 4000

Answered by mahdipoor last updated on 09/Jul/23

(1 + 2 + 3 + \dots + 100) - (2 + 4 + 6 + \dots 100)

- (5 + 10 + 15 + \dots + 100) + (10 + 20 + 30 + \dots + 100)

= \frac{100 \times 101}{2} - \frac{50 \times 102}{2} - \frac{20 \times 105}{2} + \frac{10 \times 110}{2}

= 2000

Commented by BaliramKumar last updated on 09/Jul/23

typo sir 4000 \to 2000

Nice solution

Commented by mahdipoor last updated on 09/Jul/23

y o u a r e r i g h t, i f o r g e t \frac{}{2}!

Answered by BaliramKumar last updated on 09/Jul/23

Apply {Euler}^{'} s totient function

Sum = 100 \times \frac{ϕ (100)}{2} = 100 \times \frac{40}{2} = 100 \times 20 = 2000