Question

using Euclids division algorithm, find the largest no. that divides 1251,9377 & 15628 leaving remainder 1,2,3 respectively.

Answer 1

1251 - 1 = 1250
9377 - 2 = 9375
15628 - 3 = 15625
 
H.C.F of 1250, 9375 and 15625

1250)9375(7
         8750
            _
         625)1250(2
                 1250
                     _
                     0



625)15625(25
        15625
           _
           0

Thus H.C.F (1250,9375,15625) = 625

This is the answer for your question..
You could check this by dividing 1252 , 9377 and 15628 by 625 and see if they leaves reminders 1,2and 3 respectively.