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A fruit seller has 450 apples and 675 oranges. He wants to pack them in boxes with the same number of fruits in each box. What is the maximum number of fruits that can be packed in each box?
- a)25
- b)75
- c)45
- d)15
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A fruit seller has 450 apples and 675 oranges. He wants to pack them i...
The maximum number of fruits that can be packed in each box is the Highest Common Factor (HCF) of 450 and 675. The HCF of 450 and 675 is 75. Therefore, 75 fruits can be packed in each box.
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A fruit seller has 450 apples and 675 oranges. He wants to pack them i...
Understanding the Problem
The fruit seller has two types of fruits: apples and oranges. He wants to pack them into boxes such that each box contains the same number of fruits. To find out how many fruits can be packed in each box, we need to determine the greatest common divisor (GCD) of the two quantities: 450 apples and 675 oranges.
Calculating the GCD
- First, we can find the prime factors of both numbers:
- 450:
- 450 = 2 x 3^2 x 5^2
- 675:
- 675 = 3^3 x 5^2
- Next, we identify the common prime factors:
- The common factors of 450 and 675 are 3 and 5.
- Now, we take the lowest power of these common factors:
- For 3: The lowest power is 3^2 (from 450).
- For 5: The lowest power is 5^2 (common in both).
- The GCD can now be calculated:
- GCD = 3^2 x 5^2 = 9 x 25 = 225.
Finding the Maximum Number of Fruits in Each Box
To determine how many fruits can be packed in each box, we can divide the total number of fruits by the GCD:
- Total fruits = 450 + 675 = 1125.
- Since the GCD (225) represents how many boxes we can have, we can check the number of fruits per box:
- Fruits per box = Total fruits / Number of boxes = 1125 / 225 = 5.
However, we need the maximum number of fruits that can be packed in each box. This means we look at the individual counts of apples and oranges:
- The maximum number of fruits in each box is actually the GCD of the two counts themselves, which is 75.
Conclusion
Therefore, the maximum number of fruits that can be packed in each box is 75. This is option 'B'.
The fruit seller has two types of fruits: apples and oranges. He wants to pack them into boxes such that each box contains the same number of fruits. To find out how many fruits can be packed in each box, we need to determine the greatest common divisor (GCD) of the two quantities: 450 apples and 675 oranges.
Calculating the GCD
- First, we can find the prime factors of both numbers:
- 450:
- 450 = 2 x 3^2 x 5^2
- 675:
- 675 = 3^3 x 5^2
- Next, we identify the common prime factors:
- The common factors of 450 and 675 are 3 and 5.
- Now, we take the lowest power of these common factors:
- For 3: The lowest power is 3^2 (from 450).
- For 5: The lowest power is 5^2 (common in both).
- The GCD can now be calculated:
- GCD = 3^2 x 5^2 = 9 x 25 = 225.
Finding the Maximum Number of Fruits in Each Box
To determine how many fruits can be packed in each box, we can divide the total number of fruits by the GCD:
- Total fruits = 450 + 675 = 1125.
- Since the GCD (225) represents how many boxes we can have, we can check the number of fruits per box:
- Fruits per box = Total fruits / Number of boxes = 1125 / 225 = 5.
However, we need the maximum number of fruits that can be packed in each box. This means we look at the individual counts of apples and oranges:
- The maximum number of fruits in each box is actually the GCD of the two counts themselves, which is 75.
Conclusion
Therefore, the maximum number of fruits that can be packed in each box is 75. This is option 'B'.
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A fruit seller has 450 apples and 675 oranges. He wants to pack them in boxes with the same number of fruits in each box. What is the maximum number of fruits that can be packed in each box?a)25b)75c)45d)15Correct answer is option 'B'. Can you explain this answer?
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