Find the largest number which divides 245 and 1245 leaving remainder 5 in each case

Both numbers has remainder of 5
We can start by subtracting 5 from both numbers

245-5=240
1245-5=1240

We can then proceed to find the Highest Common Factor of 240 and 1240.

One efficient method to find HCF for large numbers is by finding their product of prime factors. The diagram below shows the factor tree method

We then have
240 = 2×2×2×2×3×5 =×3×5
1240 = 2×2×2×5×31 = ×5×31

HCF = ×5=40