• Math

  cube

  Posted by Srimathy on June 17, 2023 at 12:51 pm

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

  Ankit Mishra replied 1 year, 10 months ago 2 Members · 1 Reply
• 1 Reply

• 

  Ankit Mishra

  Member

  June 22, 2023 at 2:21 pm

  To find the smallest number by which 256 can be divided so that the quotient is a perfect cube, we need to find the smallest cube number that divides 256.

  Let’s start by finding the prime factorization of 256:

  256 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 = 2^8

  For the quotient to be a perfect cube, we need to divide 256 by the highest power of 2 that is a cube. The highest power of 2 that is a cube is 2^6.

  Therefore, the smallest number by which 256 may be divided so that the quotient is a perfect cube is 2^6, which equals 64.

  So, 256 ÷ 64 = 4, and 4 is a perfect cube.

Log In to Reply