What are the numbers divisible by 991?

991, 1982, 2973, 3964, 4955, 5946, 6937, 7928, 8919, 9910, 10901, 11892, 12883, 13874, 14865, 15856, 16847, 17838, 18829, 19820, 20811, 21802, 22793, 23784, 24775, 25766, 26757, 27748, 28739, 29730, 30721, 31712, 32703, 33694, 34685, 35676, 36667, 37658, 38649, 39640, 40631, 41622, 42613, 43604, 44595, 45586, 46577, 47568, 48559, 49550, 50541, 51532, 52523, 53514, 54505, 55496, 56487, 57478, 58469, 59460, 60451, 61442, 62433, 63424, 64415, 65406, 66397, 67388, 68379, 69370, 70361, 71352, 72343, 73334, 74325, 75316, 76307, 77298, 78289, 79280, 80271, 81262, 82253, 83244, 84235, 85226, 86217, 87208, 88199, 89190, 90181, 91172, 92163, 93154, 94145, 95136, 96127, 97118, 98109, 99100

There is a total of 100 numbers (up to 100000) that are divisible by 991.
The sum of these numbers is 5004550.
The arithmetic mean of these numbers is 50045.5.

How to find the numbers divisible by 991?

Finding all the numbers that can be divided by 991 is essentially the same as searching for the multiples of 991: if a number N is a multiple of 991, then 991 is a divisor of N.

Indeed, if we assume that N is a multiple of 991, this means there exists an integer k such that:

$k \times 991 = N$

Conversely, the result of N divided by 991 is this same integer k (without any remainder):

$k = \frac{N}{991}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 991 (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 991 less than 100000):

1 × 991 = 991
2 × 991 = 1982
3 × 991 = 2973
...
99 × 991 = 98109
100 × 991 = 99100