Ex.1. The product of the two ne pro...
Question

# Ex.1. The product of the two ne product of the two numbers is 2028 and eir HCF is 13. The number of such pairs are. (1) 1 (2) 2 (3) 3 (4) 4

11th - 12th Class
Maths
Solution
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Sol. (2) Here, HCF of two numbers ( =13 ) let the numbers be ( 13 x ) and ( 13 y ), where ( x ) and ( y ) are prime to each other. Now, ( 13 x times 13 y=2028 ) ( Rightarrow x y=frac{2028}{13 times 13}=12 ) The possible pairs are : (1,13) (3, 4) (2, 6) But the 2 and 6 are not co-prime. ( therefore ) The required number of pairs ( =2 )