Multiple choice

The product of two numbers is 12960 and their HCF is 36. How many pairs of such numbers can be found?

  1. 3

  2. 4

  3. 6

  4. 2
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D Correct answer
Explanation

Let numbers be 36a and 36b where a, b are coprime. Product = 36a * 36b = 12960. ab = 12960 / 1296 = 10. Pairs of coprime factors of 10 are (1, 10) and (2, 5). There are 2 such pairs.

AI explanation

Let the two numbers be 36a and 36b, where a and b are co-prime numbers. Since their product is 12960, we have (36a) times (36b) = 12960, which simplifies to a times b = 10. The pairs of co-prime factors that multiply to 10 are (1, 10) and (2, 5). Therefore, exactly 2 pairs of such numbers can be found. The result is 2.

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