Question

[Phạm Trần Trúc Phương]

chứng tỏ rằng 6^15 x 24^8 x 3 chia hết cho 72^12. 

Answer 1

[Pham Van Hung]

\(6^{15}.24^8.3=\left(2.3\right)^{15}.\left(2^3.3\right)^8.3=2^{15}.3^{15}.2^{24}.3^8.3==2^{39}.3^{24}\)

\(72^{12}=\left(2^3.3^2\right)^{12}=2^{36}.3^{24}\)

Vì \(\left(2^{39}.3^{24}\right)⋮\left(2^{36}.3^{24}\right)\Rightarrow\left(6^{15}.24^8.3\right)⋮72^{12}\)