Question

What is the largest possible remainder when a two-digit number is divided by the sum of its digits?

Answer 1

Since a remainder is always less then the divisor, we start with the greatest possible divisors:

99 ; 9 + 9 = 18 ; 99 mod 18 = 9

98, 89 : 9 + 8 = 17 ; 89 mod 17 = 4 ; 98 mod 17 = 13 .

97, 88, 79 :

88 mod 16 = 8 ;

97 mod 16 = 1 ;

79 mod 16 = 15 , which is the largest possible remainder — any other divisor is smaller.

Answer 2

Answer:

What two digit integer(s) have a remainder of 15 when divided by the sum of it's digits? The answer is 79, and that is the only two-digit integer.