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The maximum number of devotes among which 540 oranges, 450 apples and 630 bananas can be distributed in such a way that number of oranges, apples and bananas remains the same is
- a)85
- b)90
- c)80
- d)105
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The maximum number of devotes among which 540 oranges, 450 apples and ...
Taking the HCF of the number of oranges, apples and bananas
Maximum number of devotes = 90
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The maximum number of devotes among which 540 oranges, 450 apples and ...
To find the maximum number of devotes among which 540 oranges, 450 apples, and 630 bananas can be distributed in such a way that the number of oranges, apples, and bananas remains the same, we need to find the common factors of the given numbers.
1. Find the factors of each number:
- Factors of 540: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
- Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
- Factors of 630: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
2. Find the common factors of the given numbers:
- Common factors of 540, 450, and 630: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
3. Calculate the maximum number of devotes:
- The maximum number of devotes is equal to the highest common factor of the given numbers.
- In this case, the highest common factor is 90.
- Therefore, the maximum number of devotes among which 540 oranges, 450 apples, and 630 bananas can be distributed is 90.
Thus, the correct answer is option 'B' - 90.
1. Find the factors of each number:
- Factors of 540: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
- Factors of 450: 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
- Factors of 630: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
2. Find the common factors of the given numbers:
- Common factors of 540, 450, and 630: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
3. Calculate the maximum number of devotes:
- The maximum number of devotes is equal to the highest common factor of the given numbers.
- In this case, the highest common factor is 90.
- Therefore, the maximum number of devotes among which 540 oranges, 450 apples, and 630 bananas can be distributed is 90.
Thus, the correct answer is option 'B' - 90.
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The maximum number of devotes among which 540 oranges, 450 apples and 630 bananas can be distributed in such a way that number of oranges, apples and bananas remains the same isa)85b)90c)80d)105Correct answer is option 'B'. Can you explain this answer?
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