a# n where if the sum of the digits of the # is divided by n, then the # itself is divisible by

Question

a number n where if the sum of the digits of the number is divided by n, then the number itself is divisible by

Answer 1

This rule only applies to 3 and 9 in the decimal system, but it applies to other bases when the divisibility test is for numbers one less than the base. For example, in base 8 add up the digits of a base 8 number (using base 8 arithmetic) to check for divisibility by 7. In base 10, the decimal system, 9 is one less than the base, so we can apply the rule for divisibility by 9.