The answer is maybe. A common law marriage requires a determination that two people have held themselves out as a married couple to the public for a sufficient period of time after considering a number of different factors, several of which you identified in your question. Co-habitation is a jumping off point, but in most cases doesn't get you there by itself. Consult a family law attorney for further information on your particular case.
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Colorado recognizes common law marriage but the parties have to intend to be married and hold themselves out to the community as being married. Domestic partnership is not the same as marriage.
Whether a common law marriage exists in any particular case must be reviewed by a lawyer. The question is not always simple and my addressing of the law does not constitute legal advice in any particular case