Question

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


Please give step by step explanation. ​

Answer 1

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 = $\dfrac{ 6336}{144}$

⇒ 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

Answer 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., 1×44,2×22,4×11

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

Hence two possible pairs exist.

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