Question

How smallest number can divide 648

Answer 1

To have a perfect cube, a number should have prime factors in groups of threes.

648 = (2×2×2) × (3×3×3) × 3

So we need two more of 3s, ei., (3×3) to complete the cube

So,

648 ×(3×3)= (2×2×2) × (3×3×3) × 3 ×(3×3)

5832 = (2×2×2) × (3×3×3) × (3×3×3)

cube root of 5832 = (2)×(3)×(3) =18

So, you need to multiply 648 by 9 to get a perfect cube, 5832

Second Solution :-

648 = 8 x 81 = 2^3 times 3^4

To get a perfect cube, each prime factor must be raised to a power that's a multiple of 3.

2^3 is there already, but 3^4 needs another 3^2 = 9. So you have to multiply by 9, and you get 5832, which is the cube of 2 x 3^2 = 18

Another :-

Let's look at the various cubes:

2 cubed = 8

3; 27

4; 64

etc.

so, the question is what do I multiply 648 to get a perfect cube. Just set up the equation:

648 x = ?

where ? is any perfect cube, suvh as 8, 27, 6^3, etc. and solve.