What are the numbers divisible by 1007?

1007, 2014, 3021, 4028, 5035, 6042, 7049, 8056, 9063, 10070, 11077, 12084, 13091, 14098, 15105, 16112, 17119, 18126, 19133, 20140, 21147, 22154, 23161, 24168, 25175, 26182, 27189, 28196, 29203, 30210, 31217, 32224, 33231, 34238, 35245, 36252, 37259, 38266, 39273, 40280, 41287, 42294, 43301, 44308, 45315, 46322, 47329, 48336, 49343, 50350, 51357, 52364, 53371, 54378, 55385, 56392, 57399, 58406, 59413, 60420, 61427, 62434, 63441, 64448, 65455, 66462, 67469, 68476, 69483, 70490, 71497, 72504, 73511, 74518, 75525, 76532, 77539, 78546, 79553, 80560, 81567, 82574, 83581, 84588, 85595, 86602, 87609, 88616, 89623, 90630, 91637, 92644, 93651, 94658, 95665, 96672, 97679, 98686, 99693

There is a total of 99 numbers (up to 100000) that are divisible by 1007.
The sum of these numbers is 4984650.
The arithmetic mean of these numbers is 50350.

How to find the numbers divisible by 1007?

Finding all the numbers that can be divided by 1007 is essentially the same as searching for the multiples of 1007: if a number N is a multiple of 1007, then 1007 is a divisor of N.

Indeed, if we assume that N is a multiple of 1007, this means there exists an integer k such that:

$k \times 1007 = N$

Conversely, the result of N divided by 1007 is this same integer k (without any remainder):

$k = \frac{N}{1007}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1007 (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 1007 less than 100000):

1 × 1007 = 1007
2 × 1007 = 2014
3 × 1007 = 3021
...
98 × 1007 = 98686
99 × 1007 = 99693