Question

find the the largest number that divides 31 and 99 leaving remainder 5 and 8 respectively

Answer 1

31-5= 26 The number is 26 or 13 or 2 99-8 = 91 13*7= 91 So 13 is the answer

Answer 2

99-8=91
so the hcf of 26 and 91 is=
26=2!26
     13!13
           1

91=13!91
       7!7
           1

the exclamatory mark above is the division of the hcf

so, the largest no. that divides 31 and 99 and leaves remainder 5 and 8 respectively is 13