Question

The smallest number by which 26136 should be multiplied so that the product is a perfect cube is

Answer 1

Answer:

26136 * 11 = 287496

Step-by-step explanation:

cbrt(287496)= 66

11 is the smallest natural number when multiplied will give a perfect cube of 66.

Answer 2

Answer:

The smallest number to be multiplies to 26136, to make it a perfect cube is 11.

Step-by-step explanation:

Given the number 26136.

The prime factorization of 26136,

$26136=2\times 2\times 2\times 3\times 3\times 3\times 11\times11=2^{3} \times3^{3} \times11^{2}$

A perfect cube is the number that has multiples of 3 as powers of prime factors.

Here, number of 2's is 3,  number of 3's is 3 and number of 11's is 2.

The number is not a perfect cube, to make it a perfect cube, 11 also must be taken 3 times.

So, the given number must be multiplied by 11.

Hence, to make 26136 a perfect cube, the smallest number to be multiplied is 11.

And the cube root will be $(2\times 3\times11)^{3} =2\times 3\times11=66$

Therefore, the smallest number to be multiplies to 26136, to make it a perfect cube is 11.

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