1. Given that $a$, $b$, $c$, $p$, and $q$ are positive integers, $p$ and $q$ are the remainders when $a$ and $b$ are divided by $c$, respectively. If $a > b$, and $a + b = 2(p + q)$, then $a + b + c$ must have a factor of ( ).
(A) 2
(B) 3
(C) 5
(D) Cannot be determined
-、1.B.
Let $a=m c+p, b=n c+q$.
Since $a+b=2(p+q)$, we have
$$
\begin{array}{l}
(m c+p)+(n c+q)=2(p+q), \\
(m+n) c=p+q<2 c,
\end{array}
$$

Therefore, $m+n<2$.
Since $a, b, c, p, q$ are positive integers, $m, n \in \mathbf{N}$. When $m+n=0$, $m=n=0$, then $a+b=p+q$. Also, $a+b=2(p+q)$, so $a=b=0$, which is a contradiction. When $m+n=1$, i.e., $m=1, n=0$ or $m=0, n=1$, in this case, $c=p+q$, so $a+b+c=3(p+q)$. Hence, $a+b+c$ must have a factor of 3.