Splitting Payments
Alice has a $420 debt in account A and a $315 debt in account B. She wants to write a program that will make those payments by an equal amount per day. For example, she could program these payments for $1 a day. If so, then account A would be paid off in 420 days and account B in 315 days.
Assuming that Alice will not pay attention to the program once it starts making payments, and assuming that she doesn't want to overpay ($2 a day will result in a loss of $1 in account B), what is the largest amount that Alice can program to be paid on each a day?
The answer is 105.
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1 solution
We can get the greatest common divisor by writing 4 2 0 = 3 ⋅ 7 ⋅ 5 ⋅ 4 and 9 ⋅ 5 ⋅ 7 = 3 1 5 . Match the factors that are in common and multiply one set of them. In this case, we have 3 ⋅ 5 ⋅ 7 = 1 0 5 . This means that 105 divides both numbers and, its the largest one that does that.