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Four friends have 24 , 36 , 40 and 60 coins respectively. They want to distribute all these coins among children in such a way that each friend gives equal number of coins to to each child and no child receives coins from more than one of the four friends.
What is the minimum number of children needed to above condition to hold true.?
Thanks
==> 24=(2^3)3, 36=(2^2)(3^2), 40=(2^3)5, 60=(2^2)(3)(5). The problem is asking for the Greatest common divisor. Since the GCD is the minimum value of the index, 2^2 =4 is the answer. Thus, 24=4*6(6to each 4 children), 36=4*9(9 to each 4 children), 40=4*10(10 to each 4 children), 60=4*15(15 to each 4 children). 4 is the answer.
In case of minimum number 1 would be the answer, hence the problem asks for maximum number where the answer is 4.
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