Question

Find the numbers of perfect cubes between between 1 and 1000001 which are exactly divisible by 7.

Answer 1

Dear student
$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{perfect}\mathrm{cubes}\mathrm{between}1\mathrm{and}1000001\mathrm{which}\mathrm{are}\mathrm{exactly} \\ \mathrm{divisibe}\mathrm{by}7\mathrm{must}\mathrm{be}\mathrm{cubes}\mathrm{of}\mathrm{numbers}\mathrm{between}1\mathrm{and}100\mathrm{that}\mathrm{are}\mathrm{divisible} \\ \mathrm{by}7.\mathrm{So},\mathrm{required}\mathrm{number}\mathrm{of}\mathrm{such}\mathrm{cubes}=14 \end{gathered}$$
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