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Question
There are 527 apples, 646 pears, and 748 oranges. These are to be arranged in heaps containing the same number of fruits. Find the greatest number of fruits possible in each heap. How many heaps are formed?
Solution
The given fruits = 527 apples, 646 pears, and 748 oranges
Clearly, the greatest number of fruits in each heap = H.C.F. of 527, 646 and 748 we have
| 17 | 527 |
| 31 | 31 |
| 1 |
| 2 | 646 |
| 17 | 323 |
| 19 | 19 |
| 1 |
| 2 | 748 |
| 2 | 374 |
| 11 | 187 |
| 17 | 17 |
| 1 |
∴ 527 = 17 × 31
646 = 2 × 17 × 19
748 = 2 × 2 × 11 × 17
So, the H.C.F. of 527, 646 and 748 = 17
∴ Required number of fruits in each heap = 17
Now, total number of fruits = 527 + 646 + 748
= 1921
Number of heaps = `"Total number of fruits"/"Number of fruits in one heap"`
= `1921/17`
= 113
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