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Show that 21 power n cannot …

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Show that 21 power n cannot end with the digit 0,2,4,6 and 8 for any natural number n

Posted by Vidhya Venkatachalam 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Ram Kushwah 6 years, 10 months ago

{tex}\begin{array}{l}21^{\mathrm n}=3^{\mathrm n\;}\times7^{\mathrm n}\\\mathrm{Now}\;3^{\mathrm n\;}\;\mathrm{and}\;7^{\mathrm n\;}\;\mathrm{are}\;\mathrm{always}\;\mathrm{odd}\;\mathrm{for}\;\mathrm{all}\;\mathrm{values}\;\mathrm{of}\;\mathrm n\\\mathrm{odd}\;\times\;\mathrm{odd}\;=\mathrm{odd}\\\mathrm{Hence}\;\;3^{\mathrm n\;}\times7^{\mathrm n}\;\mathrm{can}\;\mathrm{not}\;\mathrm{end}\;\mathrm{with}\;2,4,6,8\end{array}{/tex}

0Thank You

Geetanand Yadav 6 years, 10 months ago

It should have an even number as factor in it .but it is not there so it cannot end with digit 0,2,4,6,8

3Thank You

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CBSE > Class 10 > Mathematics