Joan's age was a factor of her grandfather's age for 6 consecutive years. What were her grandfather's ages
during this time?
To solve this problem, let's assume that Joan's age is denoted by J and her grandfather's age is denoted by G.
We are given that Joan's age was a factor of her grandfather's age for 6 consecutive years. This means that for each of these 6 years, Joan's age evenly divides her grandfather's age.
Let's consider the possible cases for these 6 years:
Case 1: Joan's age is 1 year old.
In this case, her grandfather's age could be 2, 3, 4, 5, 6, or 7 years old.
Case 2: Joan's age is 2 years old.
In this case, her grandfather's age could be 4, 6, 8, 10, 12, or 14 years old.
Case 3: Joan's age is 3 years old.
In this case, her grandfather's age could be 6, 9, 12, 15, 18, or 21 years old.
Case 4: Joan's age is 4 years old.
In this case, her grandfather's age could be 8, 12, 16, 20, 24, or 28 years old.
Case 5: Joan's age is 5 years old.
In this case, her grandfather's age could be 10, 15, 20, 25, 30, or 35 years old.
Case 6: Joan's age is 6 years old.
In this case, her grandfather's age could be 12, 18, 24, 30, 36, or 42 years old.
Therefore, the possible ages for Joan's grandfather during this time are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 35, 36, 42.