I am divorced and my ex wife is living in the home. The mortgage is in both of our names but I am making 100% of the payment each month. When I go to file my taxes for 2016, will I be able to deduct the mortgage interest even though I will file as single and have not lived in the home in 2016?

The IRS tax rules allow you to deduct mortgage interest paid on your principle residence. The deduction does not depend on your filing status, or vary with the owner's marital condition, whether single, married or divorced. But a divorce can complicate matters, especially if the responsibility for paying the mortgage or the ownership of the house changes,

As you can see, home mortgage interest is generally one of the most significant itemized deductions on Sch A of 1040.
The deduction for home mortgage interest and real estate taxes for the post-divorce period of the year will be determined by the terms of the judgment or settlement agreement and the form of ownership following the divorce. If the home continues to be held in some form of joint ownership, either as tenants in common or joint tenancy, you and your spouse are both entitled to take deductions for half of the mortgage interest and real estate taxes. However, if the entire interest in the marital residence is transferred to one party as part of the settlement, only that person can take the mortgage interest deduction. In your case, your ex-spouse owns the home and lives in it, but you take responsibility for the house payments, then you deduct that money as alimony on 1040; your ex-spouse would have to report the alimony as income, but could also claim the mortgage interest deduction as the owner