What’s the number?

It’s not easy having a mathematics professor as a new friend. When she invites you to her house she says, “All the houses on my side of the street are numbered consecutively in even numbers. There are six houses on my side of my block and the sum of their numbers is 9870. You don’t know which block I live on, and it’s a long, long street, but I will tell you that I live in the lowest number on my side of the block. What’s the number? Or are you just going to ring the first even-numbered doorbell for twenty blocks?

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She lives at number 1640.

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