If $A = {6,10,14,\cdots,1002}$ and $B$ is set of divisors of $360$, then what would be the number, and sum of elements in set $A \cap B$
I have no clue how to do this without actually writing down the entire set of $A$ and $B$ and manually comparing each element. Is there any better way to calculate this?
The comments have already given one way of solving it. Here's a slightly different one.
Note that $360 = 2^{3} \times 3^{2} \times 5^{1}$. Moreover, you're looking for those factors which are divisible by $2$ but not $4$. Thus, any such factor $d$ is precisely of the form $$d = 2 \times 3^{a} \times 5^{b}$$ for $0 \leqslant a \leqslant 2$ and $0 \leqslant b \leqslant 1$.
Can you see that the sum of all such factors is equal to $$2(1 + 3 + 3^2)(1 + 5)?$$