school has 96 mathematics books and 144 science books they are to be arranged in identical groups with the same number of books of each subjects in every group find the maximum number of groups possible

Answer: The maximum number of groups possible is 48.

Step-by-step solution

Step 1: Identify the mathematical requirement

Since each group must contain the exact same number of mathematics books and the same number of science books with no books left over, the number of groups must divide both 96 and 144. To maximize the number of groups, we must find the Highest Common Factor, or $\text{HCF}$ , of 96 and 144.

Step 2: Find the prime factorisation of 96 and 144

We express both numbers as products of their prime factors using the Fundamental Theorem of Arithmetic. Dividing 96 successively by 2 gives $2^5 \times 3$ , and dividing 144 successively gives $2^4 \times 3^2$ .

Step 3: Calculate the HCF

The $\text{HCF}$ is the product of the smallest power of each common prime factor involved in the numbers. The common prime factors are 2 and 3, with the lowest powers being $2^4$ and $3^1$ . Multiplying these gives 48.

Step 4: State the final conclusion

The maximum number of identical groups that can be formed is 48. In each group, there will be exactly 2 mathematics books and 3 science books.

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