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Find the total number of integer n such ...

Find the total number of integer `n` such that `2lt=nlt=2000` and H.C.F. of `n` and 36 is 1.

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If H. C. F. of integer n and 36 is 1, then n should not be divisible by 2 or 3.
Let us hrst find the numbers which are divisible by 2 or 3.
Number of integers lying in the interval [2, 2000] that are divisible by 2 is 1000 (2, 4, 6, ..., 1998, 2000).
Number of integers lying in the interval [2, 2000] that are! divisible by 3 is 666 (3, 6, 9, ..., 1995, 1998).
Number of integers lying in the interval [2, 2000] that are divisible by 6 is 333 (6, 12, 18, ..., 1992, 1998).
Total number of integers that are divisible by 2 or 3
=1000 + 666 333 = 1333
Thus, total number of integers that are neither divisible by 2 nor by 3
= 1999 -1333 = 666
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