How do you find the smallest positive integer k such that 1350k is a perfect cube?

Question

Santos Jones

Mathematics

25 February, 07:40

How do you find the smallest positive integer k such that 1350k is a perfect cube?

+3

Answers (1)

Know the Answer?

Karli Stout · Answer 1

A cube is x*x*x

prime factor 1350

1350*k

5*270*k

5*3*90*k

5*3*3*30*k

5*3*3*3*10*k

5*3*3*3*2*5*k

what value does k have to be to have three of each prime factor?

k = 5*2*2 = 20

Then 1350*20 = 27,000 = (5*3*2) ^3