1
Question
40 chairs are to be arranged in an auditorium in rows and columns such that each row contains same number of chairs. What are different types of arrangements possible?
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Solution
In order to know the different types of possible arrangements, we can write the factor pairs of 40.
Number of chairs in each row
Number of rows
Total number of chairs
40
1
40
20
2
40
10
4
40
5
8
40
8
5
40
4
10
40
2
20
40
1
40
40
Hence, total 8 arrangments can be possible.
| Number of chairs in each row | Number of rows | Total number of chairs |
| 40 | 1 | 40 |
| 20 | 2 | 40 |
| 10 | 4 | 40 |
| 5 | 8 | 40 |
| 8 | 5 | 40 |
| 4 | 10 | 40 |
| 2 | 20 | 40 |
| 1 | 40 | 40 |
Hence, total 8 arrangments can be possible.
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