Question

ii. What is the smallest number by which 17496 must be divided so that the quotient is a
perfect cube?​

Answer 1

Answer:

the number should be divided by 3

Answer 2

the smallest number by which 17496 must be divided , so that the quotient is a perfect cube

let smallest number be x

and quotient number be y3

so, 17496/x which gives 0 as remainder and y3 as quotient

so, factors of 17496=2×2×2×3×3×3×3×3×3×3

no of 2′ s are 3

no of 3 's are 7

so, factors of 17496=23×33×33×3=(2×3×3)3×3

so, smallest number is x=3

y3=(2×3×3)3

y=18

the perfect cube is y3=183 cube root of 183=18