What is the greatest number that divides 245 and 1,029, leaving a remainder of 5 in each case?

Explanation

1. 01

   Remove the remainder: $245 - 5 = 240$ and $1029 - 5 = 1024$.

2. 02

   $240 = 2^4 \times 3 \times 5$ and $1024 = 2^{10}$.

3. 03

   HCF = $2^4 = 16$, which is greater than the remainder 5, as required.