KöMaL 2015 K454

Several digits of the numbers in the operations below have been replaced with letters. Different letters stand for different digits, and identical letters stand for identical digits. No letter denotes the digit 1. $1 \cdot \mathrm{G} + 1 = \mathrm{H},$ $1\mathrm{A} \cdot \mathrm{G} + 2 = \mathrm{HG},$ $1\mathrm{AB} \cdot \mathrm{G} + 3 = \mathrm{HGF},$ $1\mathrm{ABC} \cdot \mathrm{G} + 4 = \mathrm{HGFE},$ $1\mathrm{ABCD} \cdot \mathrm{G} + 5 = \mathrm{HGFED}.$ Find the value of each letter.