Question

In a multiplication sum the multiplicand is 999 and the last three digits of the product are 193 . Other figures are missing . Complete the multiplication by supplying the missing figures .

Answer 1

Dear student,

Let the multiplier be the 3-digit number XYZ.

We know 999 times XYZ is a number with last three digits 193:
XYZ$\times$999 = ???193

999 times XYZ is 1000 times XYZ, minus 1 times XYZ:


1000$\times$XYZ$-$XYZ = ???193

1000 times XYZ is a number that ends with 3 zeros. The 3-digit number XYZ, subtracted from a number that ends with 3 zeros, equals a number with last 3 digits 193. That gives us only one possible value for XYZ:
XYZ000$-$XYZ = ???193
???193$+$XYZ = XYZ000
XYZ = 807

Hence the multiplication becomes 807$\times$999$=$806193


N.B- The multiplier is any integer with last 3 digits 807

Regards