Math and Arithmetic

# How many positive integers less than 1000 are either divisible by 2 or by 11?

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There are 544 positive integers less than 1,000 that are either divisible by two or by 11.

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## Related Questions There are 130 positive integers less than 1,000 that are divisible by seven but not divisible by 11 There are 1,000 positive integers between 1,000 and 9,999, inclusive, that are divisible by nine. you can say that 2/10 of every 10 integers is divisible by 5, so multiplying 2/10 by 100, giving you 200/1000 total integers are divisible by 5. half of all integers are odd, so divide 200/1000 by 2 is 100/1000, so you can correctly state that 100 odd integers under 1000 are divisible by 5. There are 90 integers less than 1,000 that are divisible by 11.   There are 128 integers between 100 and 1000 that are divisible by seven. The sum of the positive integers from 1,000 to 1,100 inclusive is: 106,050 The sum of the squares of the first 1000 positive odd integers (from 12 to 19992) is 1333333000. 500 numbers in the range [1, 1000] are divisible by 2.  1,2,3,4,5,6,7,8,9,10 all the way thru 1000.  1 and 2 are the only positive integers.  Using Gauss's method, 1+2+3...1000= 500x1001=500500 Answer:500500 There are 1000 integers from 1 to 1000. Only the multiples of 30 of these integers are divisible by 30, such as 30, 60, 90, 120, 150, 180, 210, 240, ..., 990. Since the LCM of 16 and 30 is 240, then only 7 integers from 1 to 1,000 are divisible by 30 but not by 16, which are 30, 60, 90, 120, 150, 180, and 210. (Prime factorization: 30 = 2 x 3 x 5 16 = 24 The LCM of 30 and 16 is 24 x 3 x 5 = 240.) There are no numbers that are divisible by 21 but not by 7 so the "or 21" part of the question can be ignored.There are 166 numbers between 1 and 1000 that are divisible by 6. However, 23 of those are also divisible by 7.So 166 - 23 = 143 numbers.  There are 12 integers: 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, 924. First integer divisible by 10 is 10 itself .So the numbers are 10,20,30,40 and so onthe sum is10+20+30+40+....+990+100010(1+2+3+4+.....+99+100)10*100*101/250500 1 2 3 4 5 6 7 8 9 10 Integers are positive or negative whole numbers. e.g -1,-2,...,-1000. or +1,...+1000. really hope this helps.   That would be equal to the sum of all positive integers less than 1000 minus the sum of all positive multiples of three that are less than 1000. That would be equal to: (1000 + 1) * (1000 / 2) - 3 * (333 + 1) * (333 / 2) = 1001 * 500 - 1000 * 166.5 = 500500 - 166500 = 334000

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