Sum of Product is me

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?




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I look flat, but I am deep. Hidden realms I shelter. Lives I take, but the food I offer. At times I am beautiful. I can be calm, angry, and turbulent. I have no heart but offer pleasure as well as death. No man can own me, yet I encompass what all men must have. What am I?

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In Canada, a mathematical puzzle must be solved in order to win the lottery to classify it as a “game of skill” not gambling.