Open In App

GATE | GATE CS Mock 2018 | Set 2 | Question 59

Like Article
Like
Save
Share
Report

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. 
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) = 142 
Number of integers less than 1000 which are multiples of 14 = floor(1000/14) = 71 
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


Quiz of this Question


Last Updated : 12 Jul, 2021
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads