We express both numbers as products of their prime factors. For 96, dividing repeatedly gives 2^5 × 3. For 144, the prime factor decomposition gives 2^4 × 3².

school has 96 mathematics books and 144 science books there to be arrange the ideal groups with the same number of books of each subject in every group find the maximum number of groups possible

Answer: 48

Step-by-step solution

Step 1: Identify the required mathematical operation

To divide 96 mathematics books and 144 science books into identical groups with an equal number of books of each subject per group, the number of groups must divide both 96 and 144 exactly. To maximize the number of groups, we need the Highest Common Factor (HCF) of 96 and 144.

Step 2: Find prime factorizations of 96 and 144

We express both numbers as products of their prime factors. For 96, dividing repeatedly gives $2^5 \times 3$ . For 144, the prime factor decomposition gives $2^4 \times 3^2$ .

Step 3: Calculate the HCF

The HCF is the product of the smallest powers of each common prime factor. The smallest power of 2 is $2^4 = 16$ and the smallest power of 3 is $3^1 = 3$ . Multiplying them gives $16 \times 3 = 48$ .

Step 4: Interpret the result in context

With 48 groups, each group will contain exactly 2 mathematics books and 3 science books, ensuring all groups are identical and no books are left over.

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