Multiple choice

The product of two numbers is 2028 and their HCF is 13. How many such pairs of numbers can be formed?

  1. 2

  2. 5

  3. 6

  4. 12

  5. 32
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A Correct answer
Explanation

Let the numbers be 13x and 13y, where x and y are coprime. Their product is 169xy = 2028, so xy = 12. Pairs of coprime factors of 12 are (1, 12) and (3, 4), resulting in two possible pairs of numbers.

AI explanation

Let the two numbers be 13x and 13y, where x and y are coprime. Their product is 13x multiplied by 13y equals 2028, which simplifies to 169xy equals 2028, meaning xy equals 12. The possible coprime pairs for (x, y) whose product is 12 are (1, 12) and (3, 4), meaning 2 such pairs of numbers can be formed.

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