Question

Two positive numbers have their HCF as 12 and their product as 6336. Choose the correct option for the number of pairs possible for the given numbers.

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is A 2

Let the numbers be 12x and 12y, where x and y are co-primes.

Product of the numbers = 144xy

$144xy=6336$

$xy=44$

44 can be written as the product of two factors in three ways, i.e., $1\times 44,2\times 22,4\times 11$

As x and y are relatively prime, (x,y) can be (1,44) or (4,11) but not (2,22).

Hence two possible pairs exist.