I1.4 Suppose $d$ is the number of positive factors of $500+c$, find the value of $d$.
$$
500+c=504=2^{3} \times 3^{2} \times 7
$$

A positive factor is in the form $2^{i} \times 3^{j} \times 7^{k}$, where $0 \leq i \leq 3,0 \leq j \leq 2,0 \leq k \leq 1$
The total number of positive factors are $(1+3)(1+2)(1+1)=24$