Josh has 16 apples and 24 oranges. He is dividing them into several identical piles. For each pile, he wants the same ratio between apples and oranges.What is the greatest number of these piles that he can have?
Question
Josh has 16 apples and 24 oranges. He is dividing them into several identical piles. For each pile, he wants the same ratio between apples and oranges.What is the greatest number of these piles that he can have?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of apples and oranges. The GCD is the largest number that can divide both numbers without leaving a remainder.
Step 1: Find the GCD of 16 (apples) and 24 (oranges). The GCD of 16 and 24 is 8.
Step 2: The GCD is the greatest number of piles Josh can have while maintaining the same ratio of apples to oranges in each pile.
So, Josh can have 8 piles of fruits with the same ratio of apples to oranges.
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