Multiple choice

The HCF of two numbers is 24. If the product of the two numbers is 11520, how many such unordered pair of numbers exists?

  1. 2

  2. 4

  3. 6

  4. 8
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A Correct answer
Explanation

Let numbers be 24a and 24b where gcd(a,b)=1. Product = 576ab = 11520. ab = 20. Pairs (a,b) such that gcd(a,b)=1: (1,20) and (4,5). There are 2 such pairs.

AI explanation

Let the two numbers be 24a and 24b, where a and b are coprime natural numbers. Their product is (24a) times (24b), so 576ab equals 11520, which simplifies to ab equals 20. The coprime pairs (a, b) whose product is 20 are (1, 20) and (4, 5), so there are 2 such unordered pairs.

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