Question

The difference of two three digit numbers is 729 and their hcf is 81. find the numbers

Answer 1

hcf is 81 .. and hcf of 2 no is also a factor of both numbers
let the no are 81a and 81b
given
81a -81b = 729
a-b = 9
81a<1000
a<12.34
a could be 12,11,10
so b should be .. 3,2,1

81b>100
b> 1.23
b could be 2,3
a could be 11 ,12

no are ..in pair either ( 891, 162) or ( 972, 243)

here 972/243 = 4 ... it's hcf = 243
our required no is 891 and 162