• Math

  CLASS8

  Posted by Shruti Thakar on June 23, 2023 at 2:12 pm

  What is the smallest number by which 256 may be divided so that the quotient is a perfect cube?

  Shobhit replied 1 year, 10 months ago 2 Members · 1 Reply

  • @math@class8
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  Shobhit

  Member

  June 23, 2023 at 2:43 pm

  256=2×2×2×2×2×2×2×2<div>=(2^3×2^3×2^2)</div><div>=(2×2)^3×2^2</div><div> </div><div>In this factorization there is no triplet for 2.</div><div>So, 256 is not a perfect cube.</div><div>∴ 256 has to be divided by 2^2=4 to make it a perfect cube.</div>

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