Question 59

The sum of two numbers is 45 and their product is 500. Their HCF is

Let the number be $$x$$ and $$(45 - x)$$

=> Product = $$x (45 - x) = 500$$

=> $$x^2 - 45x + 500 = 0$$

=> $$(x - 25) (x - 20) = 0$$

=> $$x = 25 , 20$$

Other number = $$20 , 25$$

Thus, the two numbers are = 20 and 25

$$\therefore$$ H.C.F. of 20 and 25 = 5

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