Final answer:
To make 1024 a perfect cube, we must divide it by 2, as the prime factorization of 1024 is 2^10, which simplifies to (2^3)^3 times 2^1. Dividing by the remaining 2^1 gives us a perfect cube.
Step-by-step explanation:
To find the smallest number by which 1024 should be divided to get a perfect cube, we first need to find the prime factorization of 1024. The number 1024 is a power of 2, specifically 2^10. A perfect cube is a number that can be expressed as the cube of an integer, which means its prime factors are all to the power of three.
Prime factorization: 1024 = 2^10 = (2^3)^3 × 2^1. To make 1024 a perfect cube, we must divide by the factor that is not included in the cube, which is 2^1, or simply 2. Therefore, 1024 divided by 2 is 512, and 512 is a perfect cube (8^3).
In conclusion, the smallest number to divide 1024 by to get a perfect cube is 2.