Question

Is 43904 a perfect cube? If not, find the smallest number by which 43904 must be divided so

that the product is a perfect cube.​

Answer 1

Answer:

The prime factorization of 43904 is 2 × 2 × 2 × 2 × 2 ×2 ×2 ×7 ×7× 7. As you can see 2 appears in this 7 times, so groups of three 2s can be made 2 times and still one 2 will be left and 7 appears in a group of three only. Thus the groups can be made as 2 × 2 ×2 × 2 × 2 ×2 × 2 ×7 ×7 ×7 and as you see a single 2 is left out and now it needs two more 2s to make it a perfect cube i.e. it should be multiplied by 4.