Question

find the smallest number by which 88209 can be divided so that the quotient is a perfect cube​

Answer 1

Answer:

To find the smallest number by which 88209 must be divided so that the quotient is a perfect cube, we have to find the prime factors of 88209.

88209=3×3×3×3×3×3×11×11

Prime factors of 88209 are 3,3,3,3,3,3,11,11.

Out of the prime factors of 88209, 11 cannot be considered in its perfect cube as it have only two factors of 11.

So, 11×11 is the number by which 88209 must be divided to make the quotient a perfect cube.

⇒  

11×11

88209

​  

=729

3

 

729

​  

=9

Hence, the smallest number is 121, which when divides 88209, the quotient is 729 which is a perfect cube.

Hence, the correct answer is 121.

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Answer 2

Given: A number-  88209

To find: The smallest number by which 88209 can be divided so that the quotient is a perfect cube

Solution: Using prime factorization, 88209 can be expressed as:

88209 = 3 × 3 × 3 × 3 × 3 × 3 × 11 × 11

We observe that 11 × 11 is left after grouping the factors as pairs of three identical numbers.

So, we should divide 88209 by 11 × 11 i.e., 121 so that it doesn't appear in the prime factorization.

88209 ÷ 121 = 729 (which is the cube of 9)

Hence, 121 is the smallest number by which 88209 must be divided to make the quotient a perfect cube.