The HCF of two numbers is 12, and their product is 4320. How many such pairs…

2019

The HCF of two numbers is 12, and their product is 4320. How many such pairs of numbers are possible?

  1. A.

    2

  2. B.

    4

  3. C.

    1

  4. D.

    3

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Show answer & explanation

Correct answer: B

Let the numbers be 12a and 12b, where HCF(a, b) = 1. Then 12a × 12b = 4320 ⇒ a × b = 4320 ÷ 144 = 30. Coprime pairs with product 30 are (1,30), (2,15), (3,10), (5,6). Hence, 4 pairs are possible.

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