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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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Answer» `36=2^(2)xx3^(2)` If H.C.F. of integer n and 36 is 1, then n should not be divisible by 2 or 3. Let us first find the numbers that are divisble by 2 or 3. The number of integers in the range [2, 2000] that are divisible by 2 is 1000 (2,4,6,.., 1998, 2000). The number of integers in the range [2, 2000] that are divisible by 3 is 666 (3,6, 9, .., 1995, 1998). The number of integers in the range [2, 2000] that are divisible by 6 is 333 (6, 12, 18,.., 1992, 1998). Total number of integers divisible by 2 or 3 is 1000+666-333=1333. Thus, the total number of integers that are divisible by neither 2 nor 3 is 1999-1333=666. |
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