What are the numbers divisible by 997?

997, 1994, 2991, 3988, 4985, 5982, 6979, 7976, 8973, 9970, 10967, 11964, 12961, 13958, 14955, 15952, 16949, 17946, 18943, 19940, 20937, 21934, 22931, 23928, 24925, 25922, 26919, 27916, 28913, 29910, 30907, 31904, 32901, 33898, 34895, 35892, 36889, 37886, 38883, 39880, 40877, 41874, 42871, 43868, 44865, 45862, 46859, 47856, 48853, 49850, 50847, 51844, 52841, 53838, 54835, 55832, 56829, 57826, 58823, 59820, 60817, 61814, 62811, 63808, 64805, 65802, 66799, 67796, 68793, 69790, 70787, 71784, 72781, 73778, 74775, 75772, 76769, 77766, 78763, 79760, 80757, 81754, 82751, 83748, 84745, 85742, 86739, 87736, 88733, 89730, 90727, 91724, 92721, 93718, 94715, 95712, 96709, 97706, 98703, 99700

There is a total of 100 numbers (up to 100000) that are divisible by 997.
The sum of these numbers is 5034850.
The arithmetic mean of these numbers is 50348.5.

How to find the numbers divisible by 997?

Finding all the numbers that can be divided by 997 is essentially the same as searching for the multiples of 997: if a number N is a multiple of 997, then 997 is a divisor of N.

Indeed, if we assume that N is a multiple of 997, this means there exists an integer k such that:

$k \times 997 = N$

Conversely, the result of N divided by 997 is this same integer k (without any remainder):

$k = \frac{N}{997}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 997 (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 997 less than 100000):

1 × 997 = 997
2 × 997 = 1994
3 × 997 = 2991
...
99 × 997 = 98703
100 × 997 = 99700