Question

Find largest nomber which divides 245 and 1037 leaving remainder 5 in each case

Answer 1

If I avoid the remainders, it seems like the number is divisible by (245–5=240) and (1029–5=1024). Its something like this: we know 5×1=5,5×2=10. The number 10 doesn’t go into 5 and leaves a remainder of 5, if we try to divide.
Largest number, hmm? Aren’t we looking for the HCF?
1024240=210=24×3×5

HCF(1024,240)=24=16