Question

Find the smallest positive integer 'k' such that 360k is a cube number. Can somebody please explain how to do this?

Answer 1

hi @naeema
\[ \begin{array}l\color{red}{\text{W}}\color{orange}{\text{E}}\color{#e6e600}{\text{L}}\color{green}{\text{C}}\color{blue}{\text{O}}\color{purple}{\text{M}}\color{purple}{\text{E}}\color{red}{\text{ }}\color{orange}{\text{t}}\color{#e6e600}{\text{o}}\color{green}{\text{ }}\color{blue}{\text{O}}\color{purple}{\text{p}}\color{purple}{\text{e}}\color{red}{\text{n}}\color{orange}{\text{S}}\color{#e6e600}{\text{t}}\color{green}{\text{u}}\color{blue}{\text{d}}\color{purple}{\text{y}}\color{purple}{\text{!}}\color{red}{\text{!}}\color{orange}{\text{ }}\color{#e6e600}{\text{:}}\color{green}{\text{)}}\color{blue}{\text{}}\end{array} \]

so, for 360k to be a cube number, its factors should be able to be grouped in 3.

like for 18k = 2*3*3*k, the k should be 2*2*3 so that both 2 and 3 are present 3 times. got this ?

Answer 2

\[360=2\times2\times2\times3\times3time5. (A cube no is \in the form of 2x2x2) So for 360 there are 3 2"s its ok.But only two 3s so we should add one more 3. \And 5 there is only 1 so we should add 2 more!! Ans is 3\times5\times5.\]

Answer 3

\(360=2\times2\times2\times3\times3 \times5. \\ \text { (A cube no is \in the form of 2x2x2) So for 360 there are 3 2"s its ok.But only two 3s so } \\ \text { we should add one more 3. And 5 there is only 1 so we should add 2 more!!} \\ Ans is \: \: 3\times5\times5.\)

Answer 4

thats what you wrote
and is absolutely correct!! :D

Answer 5

fnx i hope it has helped u!

Answer 6

yes, it has :D
thank you so much for helping :)
keep up the good work!

and if you have any doubts browsing this site, you can ask me :)

Answer 7

sure..