Two positive numbers have their HCF as 12 and their product as 6336. The number of pairs possible for the numbers, is

Solution:

It is given that HCF of two numbers = 12, product of the numbers = 6336.
As 12 is the HCF of two numbers, so let the numbers be 12a and 12b, where a and b are co-prime numbers.
Product of both numbers = 6336

⇒ 12 a × 12 b = 6336 ⇒ 144 a b = 6336 ⇒ a b = 6336144 ⇒ a b = 44

When a=1, b=44
When a=2, b=22
When a=4, b=11
As when a=2 and b=22 are not co-primes that is they have a factor, which is 2, other than 1, we will reject this option because then their HCF would become 2

12=24 and it would contradict the given condition.
Hence, the number of pairs possible for the numbers is 2 with a=1, b=44 and a=4, b=11 and the numbers are (12, 528) and (48, 132) respectively.
Hence, the correct option is 1.