Here all factors are in groups of 3’s (in triplets)
Therefore, 216 is a perfect cube number.
(ii) 128
2 | 128 |
2 | 64 |
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of
Here one factor 2 does not appear in a 3’s group.
Therefore, 128 is not a perfect cube.
(iii) 1000
2 | 1000 |
2 | 500 |
2 | 250 |
5 | 125 |
5 | 25 |
5 | 5 |
1 | |
Prime factors of 1000
Here all factors appear in 3’s group.
Therefore, 1000 is not a perfect cube.
(iv) 100
2 | 100 |
2 | 50 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 100
Here all factors do not appear in 3’s group.
Therefore, 100 is not a perfect cube.
(v) 46656
2 | 46656 |
2 | 23328 |
2 | 11664 |
2 | 5832 |
2 | 2916 |
2 | 1458 |
3 | 729 |
3 | 243 |
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 | |
Prime factors of
Here, all factors appear in 3’s group.
Therefore, 46656 is a perfect cube.