Human cells have 46 chromosomes. To ensure that each daughter cell receives one and only one of each chromosome, eukaryotic cells undergo a complex, multistep process called mitosis. Before mitosis can begin, eukaryotes must first replicate their DNA. This process is similar to but takes much longer than DNA replication in prokaryotes. Then, during mitosis, the replicated chromosomes line up along the center line of the cell. Tiny fibers, called spindle fibers, attach to the individual chromosomes and pull them apart, toward opposite poles of the cell, where they remain until the cell divides.
Long story short, the new skin cell will still have 46 chromosomes.