Step 1: Instead of dividing each number, we can generate the multiples of 132 and check which of the 8 given numbers show up in that list: \(132\times1=132\), \(132\times2=264\), \(132\times3=396\), \(132\times4=528\), \(132\times5=660\), \(132\times6=792\).
Step 2: Continuing the multiples: \(132\times7=924\), \(132\times8=1056\), and so on, none of which match 462, 968, 2178, or 5184. Jumping ahead, \(132\times48=6336\), which does match one of the numbers in our list.
Step 3: Comparing the generated multiples \(264,396,528,660,792,924,\ldots,6336\) against the given list \(264,396,462,792,968,2178,5184,6336\), exactly four numbers overlap: 264, 396, 792, and 6336.
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