Question

Find all 2-ding numbers each of which is divisible by the sum of its digits.

Answer 1

10 = 1 + 0 = 1
12 = 1 + 2 = 3	[12 is divisible by 3]
18 = 1 + 8 = 9	[18 is divisible by 9]
20 = 2 + 0 = 2	[20 is divisible by 2]
21 = 2 + 1 = 3
24 = 2 + 4 = 6
27 = 2 + 7 = 9
30 = 3 + 0 = 3
36 = 3 + 6 = 9
40 = 4 + 0 = 4
42 = 4 + 2 = 6
45 = 4 + 5 = 9
48 = 4 + 8 = 12
50 = 5 + 0 = 5
54 = 5 + 4 = 9
60 = 6 + 0 = 6
63 = 6 +3 = 9
70 = 7 + 0 = 7
72 = 7 + 2 = 9
80 = 8 + 0 = 8
81 = 8 + 1 = 9
84 = 8 + 4 = 12
90 = 9 + 0 = 9

It can be noted that 10 is divisible by 1, 12 is divisible by 3, and so on.

Thus, the required numbers are 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84 and 90.