Question

the lergest number which divider 53 and 57 leaving remainder 2 in each case, is​

Answer 1

Let the largest number be x.
So 53-2 and 57-2 both are divisible by x.
It means 51 and 55 both are divisible by x.
So, x = HCF of (51 and 55) = 1
Which is not possible.
Hence there exist no such number.