Donna was born in a year with exactly 15 factors and still alive and well. how old will he be on his birthday in 2018?
To determine Donna's age on her birthday in 2018, we first need to find out the year she was born. According to the given information, Donna was born in a year with exactly 15 factors and is still alive in 2018.
To find such a year, we start by listing the factors of various numbers:
1: 1
2: 1, 2
3: 1, 3
4: 1, 2, 4
5: 1, 5
6: 1, 2, 3, 6
7: 1, 7
8: 1, 2, 4, 8
9: 1, 3, 9
10: 1, 2, 5, 10
11: 1, 11
12: 1, 2, 3, 4, 6, 12
13: 1, 13
14: 1, 2, 7, 14
15: 1, 3, 5, 15
...
Upon examining the factors of various numbers, we find that 15 has exactly four factors: 1, 3, 5, and 15. Therefore, Donna was born in a year that is a perfect square (since the number of factors is odd and square numbers have an odd number of factors).
The square root of 15 is approximately 3.87, so the nearest whole number squared would be 4. Hence, Donna was born in the year 4^2 = 16.
Now, we can calculate Donna's age on her birthday in 2018:
2018 (current year) - 16 (birth year) = 2002
Therefore, Donna will be turning 2018 - 2002 = 16 years old on her birthday in 2018.