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Discrete Structures. Find the number of integers between 1 and 1000 which are (i) Divisible by 2,3 or 5 (ii) divisible by 3 only but not by 2 nor by 5

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Q. Find the number of integers between 1 and 1000 which are (i) Divisible by 2,3 or 5. (ii) Divisible by 3 only but not by 2 nor by 5.

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**1 Answer**

To get no. Divisible by 2, 3 or 5:2, 3 & 5 have common factor - 30.

Divide 1000 by 30.

Thus

33no.s are between 1 to 1000 which are divisible by 2, 3 &5.To get no. Only divisible by 3 n not by 2 & 5:1000/3 = 333 no. Divisible by 3

1000/6 = 166 no. Divisible by 2 & 3

1000/15 = 66 no. Divisible by 3 & 5

Thus no. Divided by only 3 = 333 - 166 - 66 =

10130