Question

Divide 259875 by the smallest number so that the quotient is a perfect cube. Also find the cube root of the quotient

Answer 1

Answer: The smallest number by which 259875 should be divided to make it a perfect cube is 77.

Explanation:

Let's expand the number 259875 into prime factors:

259875 = 3³ ∙ 5³ ∙ 7 ∙ 11

Since in the factorization, 7 and 11 appears only one time, we must divide the number 259875 by 7 · 11 = 77, then the quotient is a perfect cube.

259875 ÷ 77 = 3375

`\sqrt[3]{3375} =\sqrt[3]{3^(3) \cdot 5^(3) } =3 \cdot 5 = 15`