Which of the following numbers are not perfect cubes: - 216
- 128
- 1000
- 100
- 46656
- 216
- 128
- 1000
- 100
- 46656
Solution and Explanation
(i) \(216\)
Prime factors of \(216 = 2 × 2 × 2 × 3 × 3 × 3\)
Here all factors are in groups of \(3\)’s (in triplets)
Therefore, \(216\) is a perfect cube number.
(ii) \(128\)
Prime factors of \(128 = 2× 2 × 2 × 2× 2 × 2× 2\)
Here one factor \(2\) does not appear in a \(3\)’s group
Therefore, \(128\) is not a perfect cube.
(iii) \(1000\)
Prime factors of \(1000 = 2\times2\times2\times5\times5\times5\)
Here all factors appear in \(3\)’s group.
Therefore, \(1000\) is a perfect cube.
(iv) \(100\)
Prime factors of \( 100 = 2 \times 2 \times 5 \times 5\)
Here all factors do not appear in \(3\)’s group.
Therefore, \(100\) is not a perfect cube.
(v) \(46656\)
Prime factors of \(46656 =2 \times2\times2\times2\times2\times2\times3\times3\times3\times3\times3\times3\)
Here all factors appear in \(3\)’s group.
Therefore, \(46656\) is a perfect cube.
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