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) 5

Answer 1

Answer:

The number of pairs possible for the numbers = 2

Step-by-step explanation:

Let the two numbers = 12x and 12y

Where, x and y are co-primes.

To find, the number of pairs possible for the numbers = ?

∴ Product of the numbers = (12x)(12y) = 144xy

⇒ 144xy = 6336

⇒ xy = \dfrac{ 6336}{144}

144

6336

⇒ xy = 44

The 44 can be written as product of two factors

= 1 × 44, 2 × 22, 4 × 11

x and y are relatively prime, (x, y) can be (1, 44) or (4, 11).

(2, 22) is not the prime number.

Hence, the number of pairs possible for the numbers = 2