CAT Exam Model Paper 7 with solutions for free online practice

The number needs to be less than 13 × 52 = 676.
The highest power of 13 in 676! is 56.
The power of 13 in the smallest such number needs to be exactly 52. If we subtract 13 × 3 = 39 from 676, we get 637. The number 637! will be the smallest number of type N! that is completely divisible by ${13}^{52}$.
The sum of the digits of 637 is 16.