Question

Find the smallest number by which 109 85 must be divided so that the quotient is a perfect cube

Answer 1

Step-by-step explanation:

Resolving 10985 into prime factors we get

10985=5*13*13*13

Grouping the factors in triplets of equal factors we get,

10985=5×(13×13×13)

Clearly if we divide 10985 by 5, the quotient would be

2197 which is a perfect cube.

Therefore, we must divide 10985 by 5, so that the quotient 2197 is a perfect cube.