Question 471736: the number of integers between 1 and 250 that are divisible by2,5,7 is
Found 2 solutions by richard1234, robertb:
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! I'll denote {x|n} be the set of integers x <= 250 that divide n.
By inclusion-exclusion principle, the number of integers is {x|2} + {x|5} + {x|7} - {x|2,5} - {x|2,7} - {x|5,7} + {x|2,5,7} (this is so that we don't overcount or undercount certain numbers like 10 or 140).
Hence, the number of integers is 125 + 50 + 35 - 25 - 17 - 7 + 3 = 164.
Answer by robertb(5830)  (Show Source):
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