I'm not entirely sure I know what you mean by "expanded algorithm" but here is a guess:
31 * 19 = (13 * 9)+(31 * 10) = 117 + 310 = 427
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2 x 2 2 x 5 x 19 = 760
x = 12
According to division algorithm: Dividend = Divisor x Quotient + Remainder Dividend = 58 x 40 + 31 = 2341. So 2341 is the required number.
2 + 2 x 5 x 6 x 8 x 7 is the algorithm for that
4123 = 7 x 19 x 31