The difference be

Let x be the greater number and y be the smaller number.

Difference = x – y = 642 ……(1)

When the greater number is divided by a smaller number, the quotient is 8 and the remainder is 19.

According to Euclid’s division algorithm

Dividend = Divisor × Quotient + Remainder

x = y×8 + 19

x – 8y = 19 ……(2)

Subtracting equation (1) from equation(2),

7y = 623

y = 89

x – y = 642

x – 89 = 642

x = 731

Therefore, greater number is 731 and smaller number is 89.