how many numbers from 1 to 1000 are divisible by both 7 and 11?
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To know how many numbers less than a particular number, say x, are divisible by another number, say y, you just have to divide x by y and the quotient you get is your answer. Thus, there are 142 and 98 numbers less than 1000 which are divisible by 7 and 11 respectively.
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==>the number of positive integers less than 1000 that are divisible by either 7 or 11 is 142 + 90 - 12 = 220. ==>the number of positive integers less than 1000 that are divisible by exactly by one of 7 and 11 is 220 - 12 = 208.
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