No solution...
101
None exist. 100 is an even number and two consecutive integers can only add up to an odd number. This is because only 2 evens can add up to an even number and no two even numbers are consecutive. (or two odds, but no two odd numbers are consecutive either)
They are 2n+2
49, 51
No solution...
The integers are 99, 100 and 101. There is also a set of consecutive even integers whose sum is 300. That set is 98, 100 and 102.
101
None exist. 100 is an even number and two consecutive integers can only add up to an odd number. This is because only 2 evens can add up to an even number and no two even numbers are consecutive. (or two odds, but no two odd numbers are consecutive either)
They are 2n+2
The GCF of consecutive integers is 1.
49, 51
The average of the three integers is going to be -306/3 = -102. Therefore, taking one even integer from either side, -306 = (-100) + (-102) + (-104)
99, 100, and 101
All of them from 45 to 99 ... 55 integers.
100
To find the number of even integers between 100 and 1000, we first determine the number of even integers between 1 and 1000, which is half of the total integers (since every other integer is even). So, 1000/2 = 500 even integers between 1 and 1000. Next, we subtract the number of even integers between 1 and 100, which is 50 (since every other integer is even in this range as well). Therefore, there are 500 - 50 = 450 even integers between 100 and 1000.