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

1 answer:

3 0

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

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The complete question in the attached figure

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Z---------------- > number of zacks stamps collections for a stamp show
T---------------- > number of teri's stamps collections for a stamp show
P--------------- > number of pacos stamps collections for a stamp show
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number of teri's stamps collections for a stamp show was 15
number of pacos stamps collections for a stamp show was 9
In their display were 33 stamps