After 2004 until Hanako is 100 years old, find all ages of Hanako which can divide the A.D. year.
Answer
24 and 83 years old
Solution
The difference between A.D. and the age of Hanako is 2004 - 12 = 1992.
This difference is always the same number.
When AD is a multiple of the age of Hanako, 1992 of the difference is also a multiple of the age of Hanako.
Thus, answer will be when the age of Hanako is a divisor of 1992. Divisors of 1992 are 1, 2, 3, 4, 6, 8 , 12, 24, 83, 166, 249, 332, 498, 664, 996, 1992.
Among these numbers, the numbers of bigger than 12 and less than 100 are 24 and 83.
