Solution: Sum formula of arithmetic sequence:

Because the total is 456.

So the number of natural numbers is odd.

Suppose there are three, easy to push 456 =151+152+153.

After calculation, there is a group of 456 =15+16+17+...+33.

the second question

Solution: suppose it exists, let the first number be a 1, and according to the formula:

n^2+(2a 1- 1)n-4000=0

If this equation is regarded as a quadratic equation about n, then the root of the equation must be a positive integer.

So from the relationship between root and coefficient:

-(2a 1- 1) is a positive integer.

But obviously -(2a 1- 1) is not a positive integer.

So the sum of several consecutive natural numbers can't be 2000.