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प्रश्न
Determine the longest tape which can be used to measure exactly the lengths 7 m, 3 m 85 cm, and 12 m 95 cm.
उत्तर
The given lengths are:
7 meters = 7 × 100 cm = 700 cm
3 meters 85 cm = (3 × 100 + 85) cm = 385 cm
12 meters 95 cm = (12 × 100 + 95) cm = 1295 cm
The length of the required longest tape = H.C.F. of 700 cm, 385 cm, and 1295 cm.
We have,
| 2 | 700 |
| 2 | 350 |
| 5 | 175 |
| 5 | 35 |
| 7 | 7 |
| 1 |
| 5 | 385 |
| 7 | 77 |
| 11 | 11 |
| 1 |
| 5 | 1295 |
| 7 | 259 |
| 37 | 37 |
| 1 |
So, 700 = 2 × 2 × 5 × 5 × 7 = 22 × 52 × 7
385 = 5 × 7 × 11
1295 = 5 × 7 × 37
∴ H.C.F. of 700, 385 and 1295 = 5 × 7 = 35
∴ The required length of the longest tape is 35 cm.
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