Multiple choice

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.

  1. 2

  2. 3

  3. 4

  4. 5
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A Correct answer
Explanation

Let numbers be 12a and 12b where gcd(a,b)=1. Product = 144ab = 6336. ab = 44. Pairs (a,b) such that gcd(a,b)=1 are (1,44) and (4,11). Total 2 pairs.

AI explanation

Since the HCF is 12, the numbers can be written as 12x and 12y, where x and y are coprime. Their product is 12x times 12y = 144xy = 6336, which simplifies to xy = 44. The coprime pairs of factors for 44 are (1, 44) and (4, 11), giving exactly 2 possible pairs.

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