GATE | GATE CS Mock 2018 | Set 2 | Question 59
How many positive integers less than 1000 are coprime with 14?
(A) 571
(B) 142
(C) 429
(D) None of these
Answer: (D)
Explanation: For any number to be coprime with 14, it must not be a multiple of 2 and 7.Â
Number of integers less than 1000 which are multiples of 2 = 1000/2 = 500-1 = 499 (because positive integers less than 1000 -> 1 to 999)
Number of integers less than 1000 which are multiples of 7 = floor(1000/7) = 142Â
Number of integers less than 1000 which are multiples of 14 = floor(1000/14) = 71Â
A number of integers less than 1000 which are multiples of 2, 7, and 14 = 499 + 142 – 71 = 570 (removing duplicate since 14 multiples exists in 2 and 7 multiples list… )
Number of integers less than 1000 which are not multiples of 2 or 7 = 1000 – 570 = 430
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Last Updated :
12 Jul, 2021
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