What are the numbers divisible by 993?

993, 1986, 2979, 3972, 4965, 5958, 6951, 7944, 8937, 9930, 10923, 11916, 12909, 13902, 14895, 15888, 16881, 17874, 18867, 19860, 20853, 21846, 22839, 23832, 24825, 25818, 26811, 27804, 28797, 29790, 30783, 31776, 32769, 33762, 34755, 35748, 36741, 37734, 38727, 39720, 40713, 41706, 42699, 43692, 44685, 45678, 46671, 47664, 48657, 49650, 50643, 51636, 52629, 53622, 54615, 55608, 56601, 57594, 58587, 59580, 60573, 61566, 62559, 63552, 64545, 65538, 66531, 67524, 68517, 69510, 70503, 71496, 72489, 73482, 74475, 75468, 76461, 77454, 78447, 79440, 80433, 81426, 82419, 83412, 84405, 85398, 86391, 87384, 88377, 89370, 90363, 91356, 92349, 93342, 94335, 95328, 96321, 97314, 98307, 99300

There is a total of 100 numbers (up to 100000) that are divisible by 993.
The sum of these numbers is 5014650.
The arithmetic mean of these numbers is 50146.5.

How to find the numbers divisible by 993?

Finding all the numbers that can be divided by 993 is essentially the same as searching for the multiples of 993: if a number N is a multiple of 993, then 993 is a divisor of N.

Indeed, if we assume that N is a multiple of 993, this means there exists an integer k such that:

$k \times 993 = N$

Conversely, the result of N divided by 993 is this same integer k (without any remainder):

$k = \frac{N}{993}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 993 (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 993 less than 100000):

1 × 993 = 993
2 × 993 = 1986
3 × 993 = 2979
...
99 × 993 = 98307
100 × 993 = 99300