The product of two numbers is 2028 and their HCF is 13. The number of such…
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The product of two numbers is 2028 and their HCF is 13. The number of such pairs is:
- A.
1
- B.
2
- C.
3
- D.
4
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Correct answer: B
Given the product of two numbers is 2028 and their HCF is 13.
Let the numbers be 13a and 13b, where gcd(a,b) = 1.
Then (13a)(13b) = 2028 ⇒ 169ab = 2028 ⇒ ab = 12.
Find coprime factor pairs of 12.
1 and 12 (coprime)
3 and 4 (coprime)
These give the original number pairs (13×1, 13×12) = (13, 156) and (13×3, 13×4) = (39, 52). We count unordered pairs, so reversed pairs are not counted separately.
Therefore, the number of such pairs is 2.