What are the numbers divisible by 1004?
1004, 2008, 3012, 4016, 5020, 6024, 7028, 8032, 9036, 10040, 11044, 12048, 13052, 14056, 15060, 16064, 17068, 18072, 19076, 20080, 21084, 22088, 23092, 24096, 25100, 26104, 27108, 28112, 29116, 30120, 31124, 32128, 33132, 34136, 35140, 36144, 37148, 38152, 39156, 40160, 41164, 42168, 43172, 44176, 45180, 46184, 47188, 48192, 49196, 50200, 51204, 52208, 53212, 54216, 55220, 56224, 57228, 58232, 59236, 60240, 61244, 62248, 63252, 64256, 65260, 66264, 67268, 68272, 69276, 70280, 71284, 72288, 73292, 74296, 75300, 76304, 77308, 78312, 79316, 80320, 81324, 82328, 83332, 84336, 85340, 86344, 87348, 88352, 89356, 90360, 91364, 92368, 93372, 94376, 95380, 96384, 97388, 98392, 99396
- There is a total of 99 numbers (up to 100000) that are divisible by 1004.
- The sum of these numbers is 4969800.
- The arithmetic mean of these numbers is 50200.
How to find the numbers divisible by 1004?
Finding all the numbers that can be divided by 1004 is essentially the same as searching for the multiples of 1004: if a number N is a multiple of 1004, then 1004 is a divisor of N.
Indeed, if we assume that N is a multiple of 1004, this means there exists an integer k such that:
Conversely, the result of N divided by 1004 is this same integer k (without any remainder):
From this we can see that, theoretically, there's an infinite quantity of multiples of 1004 (we can keep multiplying it by increasingly larger integers, without ever reaching the end).
However, in this instance, we've chosen to set an arbitrary limit (specifically, the multiples of 1004 less than 100000):
- 1 × 1004 = 1004
- 2 × 1004 = 2008
- 3 × 1004 = 3012
- ...
- 98 × 1004 = 98392
- 99 × 1004 = 99396