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1. The product of two numbers is 2028 and their HCF is 13. The number of such of pair is = ?

A. 1

B. 2

C. 3

D. 4

Solution:

HCF = 13 (given)
Let number are 13x & 13y respectively

\begin{aligned} Also given \\ 13 x \times 13 y = 2028 \\ 13 \times 13 \times x y = 2028 \\ x y = \frac{2028}{13 \times 13} = 12 \\ ∴ Possible pairs are \\ = (1, 12) (3, 4) \end{aligned}

Only two pair are possible

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