Find the greatest number that will divide 455, 582 and 710 leaving remainders 14, 15 and 17 respectively.

Hence, the required number is 9.

Given numbers are 455, 582 and 710 and the respective remainders are 14, 15 and 17.

We have 455 – 14 = 441, 582 – 15 = 567 and 710 – 17 = 693.

Now let us find their HCF.

Common factors are 3 and 7.

∴ HCF = 3 × 7 = 21

Hence, the required number is 21.