Question

Допоможіть розв`язати задачу: Для подарунків придбали 96 шоколадок, 72 апельсини і 84 банани.Яку найбільшу кількість однакових подарунків можна з них скласти, використавши всі ці продукти?

Answer 1

96=2*2*2*2*2*3
72=2*2*2*3*3
84=2*2*3*7
НСД(96; 72; 84)=2*2*3=12
Відповідь: 12 подарунків

У кожному подарунку:
96:12=8(шоколадок)
72:12=6(апельсинів)
84:12=7(бананів)

Answer 2

Problem Analysis

To solve this problem, we need to find the maximum number of identical gifts that can be made using 96 chocolates, 72 oranges, and 84 bananas.

Solution

To find the maximum number of identical gifts, we need to determine the greatest common divisor (GCD) of the given numbers. The GCD represents the largest number that divides all the given numbers without leaving a remainder.

Let's calculate the GCD of 96, 72, and 84.

The prime factorization of each number is as follows: - 96 = 2^5 * 3^1 - 72 = 2^3 * 3^2 - 84 = 2^2 * 3^1 * 7^1

To find the GCD, we take the minimum exponent for each prime factor: - The minimum exponent of 2 is 2 (from 72 and 84). - The minimum exponent of 3 is 1 (from 96 and 72). - There is no common factor of 7.

Therefore, the GCD of 96, 72, and 84 is 2^2 * 3^1 = 12.

Hence, the maximum number of identical gifts that can be made using all the given products (96 chocolates, 72 oranges, and 84 bananas) is 12.

Conclusion

The maximum number of identical gifts that can be made using 96 chocolates, 72 oranges, and 84 bananas is 12.