The greatest number will divide 3026 and 5053 leaving remainders 11 and 13 respectively?

Required Number can be given by:
HCF of (3026 - 11) and (5053 - 13)
HCF of 3015 and 5040 = 15
To find HCF, we break the given numbers in their prime Factors
3015 = 3 × 3 × 5 × 67
5040 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7
We take common multiples in these two given numbers to get required HCF
And Common multiples are: 3 × 5
So, Required HCF = 15