2024/026) What is the largest number of consecutive positive integers whose sum is exactly 2024?

 Let the number of numbers be n and it starts at a

So we have the sum $= an + frac{n(n-1)}{2} = 2024$

Or $2an + n(n-1) = 4048$ and $a\ge 1$

Or $n(2a+n-1)=  4048 = 16 * 253 = 2^4  * 23 *11$

Now out of n and 2a+n-1 one is  even and one is odd so n = 16 ( 2a +n -1 = 253) or 1 ( 2a +n -1 = 4048)  or 11 ( 2a +n -1 = 368) or 23 ( 2a +n -1 = 176)

Clearly n = 23 is the largest giving 2a + 22 = 176 and a = 77

So   largest number of consecutive positive integers is 23 and it starts with 77