What is the greatest number which divides 784 and 857 and leaves the remainders 4 and 2, respectively?

Let's assume the greatest number is 'y' which divides 784 and 857 and leaves the remainders 4 and 2, respectively.

So 784-4 = 780

857-2 = 855

Now after subtracting the remainder with their respective number, obtained numbers 780 and 855 should be completely divisible by 'y'.

It means that the HCF of 780 and 855 should be equal to 'y'.

780 = $$3\times4\times5\times13$$

855 = $$3\times3\times5\times19$$

So y = $$3\times5$$ = 15