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The product of two numbers is 2028 and their H.C.F is 13. The number of such pairs is__________?

Correct answer: B. 2

  • A. 1
  • B. 2
  • C. 3
  • D. 4

Explanation

If the H.C.F. is 13, write the numbers as 13a and 13b, where a and b are co-prime. Then 13a x 13b = 2028, so ab = 2028/169 = 12. The co-prime factor pairs of 12 are (1, 12) and (3, 4), giving 2 pairs. Students may choose 1 by counting only the pair (1, 12).

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