What are the numbers divisible by 999?

999, 1998, 2997, 3996, 4995, 5994, 6993, 7992, 8991, 9990, 10989, 11988, 12987, 13986, 14985, 15984, 16983, 17982, 18981, 19980, 20979, 21978, 22977, 23976, 24975, 25974, 26973, 27972, 28971, 29970, 30969, 31968, 32967, 33966, 34965, 35964, 36963, 37962, 38961, 39960, 40959, 41958, 42957, 43956, 44955, 45954, 46953, 47952, 48951, 49950, 50949, 51948, 52947, 53946, 54945, 55944, 56943, 57942, 58941, 59940, 60939, 61938, 62937, 63936, 64935, 65934, 66933, 67932, 68931, 69930, 70929, 71928, 72927, 73926, 74925, 75924, 76923, 77922, 78921, 79920, 80919, 81918, 82917, 83916, 84915, 85914, 86913, 87912, 88911, 89910, 90909, 91908, 92907, 93906, 94905, 95904, 96903, 97902, 98901, 99900

There is a total of 100 numbers (up to 100000) that are divisible by 999.
The sum of these numbers is 5044950.
The arithmetic mean of these numbers is 50449.5.

How to find the numbers divisible by 999?

Finding all the numbers that can be divided by 999 is essentially the same as searching for the multiples of 999: if a number N is a multiple of 999, then 999 is a divisor of N.

Indeed, if we assume that N is a multiple of 999, this means there exists an integer k such that:

$k \times 999 = N$

Conversely, the result of N divided by 999 is this same integer k (without any remainder):

$k = \frac{N}{999}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 999 (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 999 less than 100000):

1 × 999 = 999
2 × 999 = 1998
3 × 999 = 2997
...
99 × 999 = 98901
100 × 999 = 99900