How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7 exist?
Answers
Given : natural numbers that are less or equal to 1000
To Find : How many are not multiples of 3,5, or 7
Solution:
Natural number from 1 to 1000 are 1000
Multiple of 3
= 3 , 6 ,________________999
333
Multiple of 5
5 , 10 _______________1000
200
Multiple of 7
7 , 14 ________________994
142
Multiple of 15
15 , 30 _______ 990
66
Multiple of 21
15 , 30 _______ 987
47
Multiple of 35
15 , 30 _______ 980
28
Multiple of 105
105 __________945
9
Multiple of 3 , 5 or 7
= Multiple of 3 + Multiple of 5 + Multiple of 7 - Multiple of 15 - Multiple of 21 - Multiple of 35 + Multiple of 105
= 333 + 200 + 142 - 66 - 47 - 28 + 9
= 543
that are not multiples of 3,5, or 7 = 1000 - 543 = 457
457 natural numbers that are less or equal to 1000 and that are not multiples of 3,5, or 7 exist
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