2. (10 points) Divide the natural numbers from 1 to 8 into two groups, such that the difference between the sums of the numbers in each group is 16. There are $\qquad$ different ways to do this.
【Analysis】According to the problem, the sum of the two groups is $(1+8) \times 8 \div 2=36$, because the difference in the sums of the natural numbers in each group is 16, so the larger group's sum is $(36+16) \div 2=26$, and the smaller group's sum is $36-26=10$, from which we can derive the solution.

【Solution】Solution: The sum of the two groups is:
$$
\begin{aligned}
& (1+8) \times 8 \div 2 \\
= & 9 \times 8 \div 2 \\
= & 36
\end{aligned}
$$

The larger group's sum is:
$$
\begin{aligned}
& (36+16) \div 2 \\
= & 52 \div 2 \\
= & 26
\end{aligned}
$$

The smaller group's sum is:
$$
36-26=10
$$

Since $10=2+8=3+7=4+6=1+2+7=1+3+6=1+4+5=2+3+5=1+2+3+4$
correspondingly $26=1+3+4+5+6+7=1+2+4+5+6+8=1+2+3+5+7+8=3+4+5+6+8=2+4+5+7+8=$
$$
2+3+6+7+8=1+4+6+7+8=5+6+7+8
$$

Therefore, there are 8 different ways to divide.
The answer is: 8.