what is the least number of cubes that can be formed by completely cutting a large cube into smaller cubes that are identical to each other
2
4
6
8
16
To find the least number of cubes that can be formed by completely cutting a large cube into smaller cubes that are identical to each other, we need to consider the factors of the large cube's volume.
First, let's analyze the options provided:
- 2: This would mean the large cube has a volume of 2. However, a cube with a volume of 2 cannot be divided into identical smaller cubes.
- 4: This would mean the large cube has a volume of 4. It is possible to divide a large cube with a volume of 4 into smaller cubes with a volume of 1, resulting in 4 identical smaller cubes.
- 6: This would mean the large cube has a volume of 6. It is not possible to divide a large cube with a volume of 6 into identical smaller cubes.
- 8: This would mean the large cube has a volume of 8. Similar to the case with 4, we can divide a large cube with a volume of 8 into smaller cubes with a volume of 1, resulting in 8 identical smaller cubes.
- 16: This would mean the large cube has a volume of 16. We can divide a large cube with a volume of 16 into smaller cubes with a volume of 1, resulting in 16 identical smaller cubes.
Therefore, the least number of cubes that can be formed by completely cutting a large cube into smaller cubes that are identical to each other is 4.