Question 7

What is the smallest number by which 3087 must be divided, so that the number obtained is a perfect cube?

Solution

The prime factorisation is $$3087 = 3^2 \times 7^3$$. The factor $$7^3$$ is already a cube, so we must remove $$3^2 = 9$$. Then $$\frac{3087}{9} = 343 = 7^3$$, a perfect cube.

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