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प्रश्न
A trader has three bundles of string 392 m, 308 m and 490 m long. What is the great est length of string that the bundles can be cut up into without any left over string?
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उत्तर
The greatest length of string that the bundles can be cut up into without any left over the string is given by the HCF of 392, 308, and 490.
| 2 | 392 |
| 2 | 196 |
| 2 | 98 |
| 7 | 49 |
| 7 | 7 |
| 1 |
| 2 | 308 |
| 2 | 154 |
| 7 | 77 |
| 11 | 11 |
| 1 |
| 2 | 490 |
| 5 | 245 |
| 7 | 49 |
| 7 | 7 |
| 1 |
392 = 2 × 2 × 2 × 7 × 7
308 = 2 × 2 × 7 × 11
490 = 2 × 5 × 7 × 7
∴ HCF = 2 × 7 = 14
Hence, the greatest length of string that the bundles can be cut up into without any left-over string is 14 m.
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