Multiple choice

The HCF and product of two numbers are 15 and 6300 respectively, the number of possible pairs of the numbers is

  1. 4

  2. 3

  3. 2

  4. 1
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C Correct answer
Explanation

Let numbers be 15x and 15y where gcd(x,y)=1. Product = 15x * 15y = 225xy = 6300. xy = 6300/225 = 28. Pairs (x,y) such that gcd(x,y)=1 are (1,28) and (4,7). There are 2 pairs.

AI explanation

Since the highest common factor is 15, the two numbers can be written as 15x and 15y, where x and y are coprime. Their product is 15x times 15y, which equals 225xy, and we know the product is 6300. Dividing 6300 by 225 gives xy = 28. The pairs of coprime factors for 28 are (1, 28) and (4, 7), yielding exactly 2 possible pairs of numbers.

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