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Q: What are the numbers less than 1000 that are divisible by 15 20 and 35?

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There are 83 numbers less than 1,000 that are divisible by both three and four.

333 of them.

From 1 (inclusive) to 1000(inclusive,) 750.

858

130 numbers

There are 90 integers less than 1,000 that are divisible by 11.

How many numbers less than 700 are divisible by both 15 and 21?

There are 130 positive integers less than 1,000 that are divisible by seven but not divisible by 11

1000 ÷ 8 = 125 → largest less than 1000 divisible by 8 is 124 x 8 = 992

55,50,45,40,35,30,25,20,15,10,5

75,000,000,000 of them.

There are 8 odd numbers less than 50 that are divisible by 3 They are 3, 9, 15, 21, 27, 33, 39, and 45.

17 odd numbers.

The numbers that are divisible by both 3 and 5 have to be a factor of 15. That leaves 15, 30, 45, 60, 75, and 90. There are 6 numbers less than 100 divisible by 3 and 5

333 (including 3 itself).

18 numbers are there

666 integers.

They are all the numbers divisible by 2 with no remainder

8 of the numbers less than 660 are divisible by 5 and 11 but not 3. All numbers divisible by 5 and 11 are multiples of their lcm; lcm(5, 11) = 55 All numbers divisibile by 5, 11 and 3 are multiples of their lcm; lcm(5, 11, 3) = 165 659 ÷ 55 = 11 54/55 → 11 numbers less than 660 are divisible by 5 and 11 659 ÷ 165 = 3 164/165 → 3 numbers less than 660 are divisible by 5, 11 and 3 → of the 11 numbers less than 660 divisible by 5 and 11, 3 are also divisible by 3 → 11 - 3 = 8 numbers less than 660 are divisible by 5 and 11 but not 3,.

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

14. Assuming dealing with only counting numbers (ie integers greater than 0): Numbers divisible by 5 or 7 are their multiples. 50 ÷ 5 = 10 → last multiple of 5 less than 50 is 9 x 5 → 9 numbers less than 50 are divisible by 5 50 ÷ 7 = 71/7 → last multiple of 7 less than 50 is 7 x 7 → 7 numbers less than 50 are divisible by 7 Numbers divisible by both are those which are multiples of their lowest common multiple = 35 50 ÷ 35 = 115/35 → last multiple of 35 less than 50 is 1 x 35 → 1 number less than 50 is divisible by both 5 and 7 and needs to be removed from both the above counts. → (9 - 1) + (7 - 1) = 14 numbers less than 50 are divisible by 5 or 7 but not both. If there is no restriction on numbers being greater than 0, there are infinitely many numbers as it includes the infinite number of negative numbers which are all less than 50 and provide an infinite number of numbers divisible by 5 or 7 but not both.

There are 168 prime numbers less than 1,000.

56 of them.

{3,6,9,12,15,18,21,24}

19

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