Which of the following is a cube of an odd number?
From the prime factorization of 216, we get,
2 | 216 |
2 | 108 |
2 | 54 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
216 = 2×2×2×3×3×3
From the prime factorization of 512, we get,
2 | 512 |
2 | 256 |
2 | 128 |
2 | 64 |
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
From the prime factorization of 343, we get,
7 | 343 |
7 | 49 |
7 | 7 |
1 |
343 = 7×7×7
From the prime factorization of 1000, we get,
2 | 1000 |
2 | 500 |
2 | 250 |
5 | 125 |
5 | 25 |
5 | 5 |
1 |
216 = 6 × 6 × 6
512 = 8 × 8 × 8
343 = 7 × 7 × 7
1000 = 10 × 10 × 10
Hence, we can see clearly that 343 is a cube of an odd number.