The grandmother is 63 and the grandson is 15.
You must find numbers that multiply up to 945:
Ex:
45*21=495
135*7=495
63*15=495
If their products = 946 you must find 2 numbers that it would be reasonable for a grandson and grandmother to be. First of all find all the prime factors of 945.
945: 5 * 3 * 3 * 3 * 7
Now you have no other information that we could use to find the ages of grandson and grandmother except common sense. There is no clue how to divide 3 * 3 * 3 * 5 * 7. Such a result is called a Diophantine condition. For example, you could use 3*3*3* 5*7 which would give 27 * 35. It's possible, but it is not reasonable. 27 years ago, just as the grandson is being born, his grandmother would be 8 years old. There must be something more reasonable.
Remember that all primes have to be used.
How about we try 3*5 and 3*3*7. That would make the grandson 15 and his grandmother 63. She would be 48 when he was born. Isn't that much much more reasonable? So common sense (and Diophantine) would pick this as an answer. If you find something you like better, use it. After all, who can argue with you?
