To determine which of the given numbers divides 5,63,607, we need to check divisibility rules for each option.

1. Divisibility by 8: A number is divisible by 8 if the last three digits form a number that is divisible by 8.
   • The last three digits of 5,63,607 are 607.
   • 607 divided by 8 gives 75.875, which is not an integer, so 607 is not divisible by 8.
   • Therefore, 5,63,607 is not divisible by 8.
2. Divisibility by 10: A number is divisible by 10 if it ends with 0.
   • 5,63,607 ends with 7, not 0.
   • Therefore, 5,63,607 is not divisible by 10.
3. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
   • The sum of the digits of 5,63,607 is \(5 + 6 + 3 + 6 + 0 + 7 = 27\).
   • 27 divided by 3 gives 9, which is an integer.
   • Therefore, 5,63,607 is divisible by 3.
4. Divisibility by 13: For divisibility by 13, manual division is typically used as there is no simple standard rule.
   • 5,63,607 divided by 13 gives approximately 43354.3846, which is not an integer.
   • Therefore, 5,63,607 is not divisible by 13.

Based on the divisibility tests above, the number that divides 5,63,607 is 3.