Subtract 1, 2, 3 from 1251, 9377, 15628 respectively.

1251 - 1 = 1250,

9377 - 2 = 9375,

15628 - 3 = 15625

Find the HCF of 1250 and 9375

9375 = 1250 x 7 + 625

1250 = 625 x 2 + 0

thus 625 is the HCF

Now, find the HCF of 625 and 15625

15625 = 625 x 25 + 0

Thus 625 is the number that divides 1251, 9377 and 15628 leaving the remainders 1, 2 and 3 respective.