Ariell has 36 chemistry books, 32 biology books and 28 physics books. She wishes to arrange the books in groups such that each group has the same number of each book without any book being left out. Calculate the maximum number of books that can be found in each group.
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To determine the maximum number of books that can be found in each group, we need to find the greatest common divisor (GCD) of the three numbers: 36, 32, and 28.
The prime factorization of 36 is 2^2 * 3^2.
The prime factorization of 32 is 2^5.
The prime factorization of 28 is 2^2 * 7.
To find the GCD, we take the highest power of each prime factor that is present in all three numbers.
The highest power of 2 that is common to all three numbers is 2^2 = 4.
There is no common factor of 3 among the three numbers.
There is no common factor of 7 among the three numbers.
Thus, the GCD of 36, 32, and 28 is 2^2 = 4.
Therefore, the maximum number of books that can be found in each group is 4.
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