Question

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

Answer 1

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).