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Question Number 193045 by Trent1111 last updated on 02/Jun/23
what is the HCF of   8k+1 and 9k ? where k ∈ Z^+
$${what}\:{is}\:{the}\:{HCF}\:{of}\: \\ $$$$\mathrm{8}{k}+\mathrm{1}\:{and}\:\mathrm{9}{k}\:?\:{where}\:{k}\:\in\:\mathbb{Z}^{+} \\ $$
Answered by MM42 last updated on 02/Jun/23
(8k+1,9k)=d  d∣8k+1 ⇒d∣72k+9     d∣9k⇒d∣72k  ⇒d∣9⇒d=1 ∨ 3 ∨ 9
$$\left(\mathrm{8}{k}+\mathrm{1},\mathrm{9}{k}\right)={d} \\ $$$${d}\mid\mathrm{8}{k}+\mathrm{1}\:\Rightarrow{d}\mid\mathrm{72}{k}+\mathrm{9}\:\:\: \\ $$$${d}\mid\mathrm{9}{k}\Rightarrow{d}\mid\mathrm{72}{k} \\ $$$$\Rightarrow{d}\mid\mathrm{9}\Rightarrow{d}=\mathrm{1}\:\vee\:\mathrm{3}\:\vee\:\mathrm{9} \\ $$
Commented by Trent1111 last updated on 02/Jun/23
thanks sir so much   can you recommend me what concept to study
$${thanks}\:{sir}\:{so}\:{much}\: \\ $$$${can}\:{you}\:{recommend}\:{me}\:{what}\:{concept}\:{to}\:{study} \\ $$$$ \\ $$
Commented by MM42 last updated on 02/Jun/23
what age group are you?
$${what}\:{age}\:{group}\:{are}\:{you}? \\ $$

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