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

A. 3 B. 4 C. 2 D. 1

Your Answer

The answer is c)2
    Given:
         The product of two numbers is 2028.
                i.e.  XY=2028
         The prime factorisation of 2028 are 2,2,3,13,13.
           The hcf of two number is 13.
                X=13(A)          Y=13(B)
           From the prime factorisation ,the combinations formed are 
                1)X=13(1)        Y=13(2*2*3)
                 2)X=13(2)       Y=13(2*3)
                 3)X=13(2*2)     Y=13(3)
             1) AND 3) have the HCF 13.2)have HCF 26.
             Hence there are totally 2 pairs available.(13,2028),(52,39)

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