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