Greta is making fruit baskets. She has 64 apples and 96 oranges. Greta wants to make all the fruit baskets identical without having any pieces of fruit left over. What is the greatest number of fruit baskets Greta can make?
Question
Greta is making fruit baskets. She has 64 apples and 96 oranges. Greta wants to make all the fruit baskets identical without having any pieces of fruit left over. What is the greatest number of fruit baskets Greta can make?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of apples (64) and oranges (96). The GCD is the largest number that divides both numbers without leaving a remainder.
Here are the steps to find the GCD:
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List the prime factors of each number:
- Prime factors of 64: 2, 2, 2, 2, 2, 2 (since 2^6 = 64)
- Prime factors of 96: 2, 2, 2, 2, 2, 3 (since 2^5 * 3 = 96)
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Identify the common prime factors:
- The common prime factors are: 2, 2, 2, 2, 2 (five 2's)
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Multiply the common prime factors to get the GCD:
- GCD = 2 * 2 * 2 * 2 * 2 = 32
So, the greatest number of identical fruit baskets Greta can make is 32.
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