Choose the correct answer.A fruit store had 60 pears, 72 oranges and 108 plums. The owner packed all the fruits into bags with the same number of each type of fruits. Find the maximum number of bags he packed.19 bags17 bags14 bags12 bags
Question
Choose the correct answer.A fruit store had 60 pears, 72 oranges and 108 plums. The owner packed all the fruits into bags with the same number of each type of fruits. Find the maximum number of bags he packed.19 bags17 bags14 bags12 bags
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the numbers 60 (pears), 72 (oranges), and 108 (plums). The GCD is the largest number that can divide all these numbers without leaving a remainder.
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First, let's find the factors of each number:
- The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
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Now, let's find the common factors of these three numbers:
- The common factors are: 1, 2, 3, 4, 6, 12
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The greatest common factor (GCF) or greatest common divisor (GCD) is 12.
So, the owner can pack the fruits into 12 bags with the same number of each type of fruits. Therefore, the correct answer is "12 bags".
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