Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers,
Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers, is :
(a) 2
(b) 3
(c) 4
(d) 1
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Correct answer is (a) 2
Let the number be 12x and 12y, where x and y are co-primes.
Product of the numbers = 144 xy
144 xy = 6336
xy \(=\frac{6336}{144}\) = 44
44 can be written as the product of two factors in three ways, 1 × 44, 2 × 22, 4 × 11
As x and y are relatively prime. (x, y) can be (1, 44) or (4, 11) but not (2, 22).
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