There are an infinite number of possible answers:
1 + 123, 2 + 122, 3 + 121 etc
then
1.1 + 122.9, 1.2 + 122.8 etc
and
1.01 + 122.99, 1.02 + 122.98 etc
And then you could include negative numbers:
125 - 1, 126 - 2, etc
and also irrationals: 1+sqrt(2), 123-sqrt(2), etc
etc
And that is only pairwise addition. You could add 3, 4, 5 ... an infinite number of numbers!
Edit: If you mean whole numbers (excluding integers and all that other junk), then... do you mean how many pairs of numbers add up to 124?
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130 add up numbers (780) divide by number of numbers you added (6)
122, 123, 124, 125, 126. The only way for the mean of 5 consecutive numbers to be 124 is if the median is also 124.
There is an infinite number of numbers which are not factors of 124. They are all numbers apart from 1, 2, 4, 31, 62, 124.
the mean is the average of the numbers. Since the mean of the 4 numbers is 24.5, the sum of the numbers is 4 x 24.5 = 98. If you add 26 the sum is 98 + 26 =124, and the new mean is the average of the 5 numbers, or 124/5 = 24.8
-- Any number less than 124 can go into 124, but most of them can't go into it evenly.-- The numbers that go into 124 evenly are: 1, 2, 4, 31, 62, and 124.