1. Let $a=\sum_{i=1}^{24}[\sqrt{i}]([x]$ denotes the greatest integer not exceeding the real number $x$), and the set $A=\left\{x\left|x \in \mathbf{Z}_{+}, x\right| a\right\}$. Then the number of elements in set $A$ is ( ).
(A) 4
(B) 6
(C) 8
(D) 12
- 1. C.

Notice,
$$
\begin{aligned}
a= & \sum_{i=1}^{24}[\sqrt{i}] \\
= & ([\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}])+ \\
& ([\sqrt{4}]+[\sqrt{5}]+\cdots+[\sqrt{8}])+ \\
& ([\sqrt{9}]+[\sqrt{10}]+\cdots+[\sqrt{15}])+ \\
& ([\sqrt{16}]+[\sqrt{17}]+\cdots+[\sqrt{24}]) \\
= & 1 \times 3+2 \times 5+3 \times 7+4 \times 9 \\
= & 70=2 \times 5 \times 7 .
\end{aligned}
$$

Thus, the number of elements in set $A$ is the number of subsets of $\{2,5,7\}$, which is $2^{3}=8$.