What are the numbers divisible by 749?

749, 1498, 2247, 2996, 3745, 4494, 5243, 5992, 6741, 7490, 8239, 8988, 9737, 10486, 11235, 11984, 12733, 13482, 14231, 14980, 15729, 16478, 17227, 17976, 18725, 19474, 20223, 20972, 21721, 22470, 23219, 23968, 24717, 25466, 26215, 26964, 27713, 28462, 29211, 29960, 30709, 31458, 32207, 32956, 33705, 34454, 35203, 35952, 36701, 37450, 38199, 38948, 39697, 40446, 41195, 41944, 42693, 43442, 44191, 44940, 45689, 46438, 47187, 47936, 48685, 49434, 50183, 50932, 51681, 52430, 53179, 53928, 54677, 55426, 56175, 56924, 57673, 58422, 59171, 59920, 60669, 61418, 62167, 62916, 63665, 64414, 65163, 65912, 66661, 67410, 68159, 68908, 69657, 70406, 71155, 71904, 72653, 73402, 74151, 74900, 75649, 76398, 77147, 77896, 78645, 79394, 80143, 80892, 81641, 82390, 83139, 83888, 84637, 85386, 86135, 86884, 87633, 88382, 89131, 89880, 90629, 91378, 92127, 92876, 93625, 94374, 95123, 95872, 96621, 97370, 98119, 98868, 99617

There is a total of 133 numbers (up to 100000) that are divisible by 749.
The sum of these numbers is 6674339.
The arithmetic mean of these numbers is 50183.

How to find the numbers divisible by 749?

Finding all the numbers that can be divided by 749 is essentially the same as searching for the multiples of 749: if a number N is a multiple of 749, then 749 is a divisor of N.

Indeed, if we assume that N is a multiple of 749, this means there exists an integer k such that:

$k \times 749 = N$

Conversely, the result of N divided by 749 is this same integer k (without any remainder):

$k = \frac{N}{749}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 749 (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 749 less than 100000):

1 × 749 = 749
2 × 749 = 1498
3 × 749 = 2247
...
132 × 749 = 98868
133 × 749 = 99617