How can you determine the factors of the sum of two cubes?

Answer 1

Completely factorise the given number. Then group its factors into sets of 3. Take just one representative from each set and multiply these together. The answer is the required cube root.

For example,

1728 = 2*2*2*2*2*2*3*3*3 = (2*2*2)*(2*2*2)*(3*3*3)

So, the cuberoot is = 2 * 2 * 3 = 12

Answer 2

Perfect cubes have prime factors in multiples of 3.

3 x 3 x 3 = 27

2 x 2 x 2 x 5 x 5 x 5 = 1000

Answer 3

a3 + b3 = (a + b)*(a2 - ab + b2) which gives an initial factorisation as shown in the two brackets. Each of these may have further factors.

Answer 4

The prime numbers total the number you started with.

2 x 2 x 3 x 3 = 36