The new numbers after subtracting remainders are:

626-1 = 625

3127-2 = 3125

15628-3 = 15625

Prime factors of 625 = 5 × 5 × 5 × 5

Prime factors of 3125 = 5 × 5 × 5 × 5 × 5

Prime factors of 15625 = 5 × 5 × 5 × 5 × 5 ×x 5

Therefore HCF of 625, 3125 and 15625 is: 5 × 5 × 5 × 5= 625

Hence the largest number which divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively is 625