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 × 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
