Cubes

Units Digits in Cube Numbers

Depending on whether a number is odd or even, its cube number is also odd or even respectively.
This is determined by the nature of the cube numbers’ unit digit.

  • If a number is odd, its cube numbers’ unit digit is also odd.
  • If a number is even, its cube numbers’ unit digit is also even.

The table below shows the units digit of a number and the units digit of the cube of that number:

Units digit of numberUnits digit of its cube
11
28
37
44
55
66
73
82
99

Prime Factorisation Method to Find a Cube

In the prime factorisation of any number, if each prime factor appears three times, then the number is a perfect cube.

Consider, the number 216. By prime factorisation,
216=2\times2\times2\times3\times3\times3=2^3\times3^3=6^3

Hence, 216 is a perfect cube.

Consider, the number 500. By prime factorisation,
500=2\times2\times5\times5\times5=2^2\times5^3
In the above prime factorisation 2 appears twice.
Hence, 500 is not a perfect cube.

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