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Question Number 95325 by ~blr237~ last updated on 24/May/20

$$\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}HCF(20,n)=0?$$

Commented by mr W last updated on 24/May/20

$$1⩽HCF(20,n)⩽20forn⩾20$$$$\frac{1}{n}⩽\frac{HCF(20,n)}{n}⩽\frac{20}{n}$$$$\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}⩽\underset{n\to \mathrm{\infty }}{\lim }\frac{HCF(20,n)}{n}⩽\underset{n\to \mathrm{\infty }}{\lim }\frac{20}{n}$$$$0⩽\underset{n\to \mathrm{\infty }}{\lim }\frac{HCF(20,n)}{n}⩽0$$$$\Rightarrow \underset{n\to \mathrm{\infty }}{\lim }\frac{HCF(20,n)}{n}=0$$

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