Computer-Networks

14 can be written as 7×2. So any no. which is co-prime to 14 should not be divisible by 7 nor divisible by 2.
Let’s first find no. of numbers divisible by 7 or 2.
Let the no. of numbers divisible by 7 is A, and no. of numbers divisible by 2 is B.
Now no. numbers divisible by 7,
A = 999/7 = 142
No. of numbers divisible by 2 is,
B = 999/2 = 499
No. of numbers divisible by both 7 and 2, i.e., 14
A∩B = 999/14 = 71
∴ No. of numbers divisible by 7 or 2 is
A∪B = A + B – A∩B = 142 + 499 – 71 = 570
∴ No. of numbers that are coprime to 14 are,
999 – 570 = 429