math
posted by ayan .
Calvin and Ken bought a bag of 60 onions. They divide all of these onions between them, such that the number of onions that Ken has is a multiple of the number of onions that Calvin has. Given that Calvin has at least 7 onions, what is the maximum number of onions that Ken has?

the factors of 60 are 2,3,4,6,10,15,20,30
so, if Calvin has c onions (c >= 7),
c must be a factor of 60, since c and some multiple of c add to 60.
The maximum for Ken means the minimum for Calvin.
So, if Calvin has 10, then Ken has 50, the max.
There are no other factors of 60 less than 10, but greater than 7.
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