Question Number 215231 by Mingma last updated on 01/Jan/25
Answered by A5T last updated on 01/Jan/25
$$\mathrm{2024}=\mathrm{8}×\mathrm{253}=\mathrm{8}×\mathrm{11}×\mathrm{23} \\ $$$$\mathrm{2025}=\mathrm{45}^{\mathrm{2}} =\mathrm{3}^{\mathrm{4}} ×\mathrm{5}^{\mathrm{2}} ;\:\:\:\:\mathrm{2026}=\mathrm{2}×\mathrm{1013} \\ $$$$\Rightarrow\mathrm{smallest}\:\mathrm{perfect}\:\mathrm{square} \\ $$$$=\:\mathrm{2}^{\mathrm{4}} ×\mathrm{3}^{\mathrm{4}} ×\mathrm{5}^{\mathrm{2}} ×\mathrm{11}^{\mathrm{2}} ×\mathrm{23}^{\mathrm{2}} ×\mathrm{1013}^{\mathrm{2}} \\ $$$$\mathrm{which}\:\mathrm{has}\:\mathrm{5}^{\mathrm{2}} ×\mathrm{3}^{\mathrm{4}} =\mathrm{2025}\:\mathrm{positive}\:\mathrm{factors}. \\ $$
Commented by Mingma last updated on 01/Jan/25
Perfect ��