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Age. You have to stop claiming your child when she turns 19, unless she goes on to become a full-time student. In that case, you keep claiming the exemption until she's 24, as long as she meets the other qualifying-child tests. After a child reaches age 24, you can only claim her if she's completely and totally disabled.
The Basics of the Child Tax Credit. You can claim the child tax credit for each of your children under the age of 17. Some other rules apply as well, so all your dependents may not necessarily qualify. Qualifying for and claiming the child tax credit can reduce any tax you owe to zero.