How many children are you allowed to file and how many children do you actually get credit for

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There is not a limit of how many children you can claim as dependents.  There is a limit of three children for the earned income credit.  So even if you have more than three kids you cannot get more EIC.  But there are other child-related credits.  Enter all of the children who qualify as your dependents on your tax return and let TurboTax do the calculations.