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The sum of two numbers is 216 and their HCF is 27. How many pairs of such numbers are there?
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- 1
- 2
- 3
- 0
Correct Option: B
Given that , HCF of two numbers = 27
∴ Let the numbers be 27p and 27q where p and q are prime to each other.
According to the question ,
27p + 27q = 216
⇒ 27 (p + q) = 216
| ⇒ p + q = | = 8 | 27 |
∴ Possible pairs of p and q = (1 , 7) and (3 , 5)
∴ Numbers = (27 , 189) and (81 , 135)
Hence , required answer is 2 .
