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For tax purposes, how you finance your investment is irrelevant. Mortgage is not taken in consideration when calculating your capital gains.
If you do 1031 exchange but only reinvest 1/2 of the proceeds you will have capital gains to report. How much it will depend on your basis (original purchase, improvements, depreciation you took an such).
For the 1031 to be completely tax free, you will have to use the entire proceeds to purchase a replacement property. If you keep some of the proceeds (receive a "boot") the proceeds will be taxable. If you replace 1M property with a 500K property, you will have 500K boot. It doesn't matter if you get a mortgage or not.
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