Question

Find the smallest number by which \[3087\] must be multiplied so that the product is a perfect cube.

Answer 1

Hint:
In this type of question, we just need to do first the factorization of the number, and then we have to find the triplet so if there will be the triplet we can say that the number is a perfect cube and if not then to make it triplet we will multiply the missing number and in this way, we can find the number.

Complete step by step solution:
 The prime factorization \[3087\] will be equal to
\[ \Rightarrow 3087 = 3 \times 3 \times 7 \times 7 \times 7\]
So the above number can also be written in the form of power. So we get
\[ \Rightarrow 3087 = {3^2} \times {7^3}\]
From this, we can see that no triplet $3$ is present in the factorization \[3087\].
Therefore, we can also say that \[3087\] does not have a cube root, and hence to make it cube root we just need to multiply the factorization by $3$. Because it will complete the triplet.

Therefore, the number which will be the smallest number by which \[3087\] is to be multiplied so that the product has a cube root will be equal to $3$.

Additional information:
Firstly, we’ll see what ‘factorization’ is. Factorization is, simply put, splitting a number into ‘factors’, such that the product of all these factors returns the original number. Also, we can say that the breaking down of a single number to find the “root” numbers that when multiplied back, equal the original number.

Note:
For solving these types of questions we just need to be careful while solving the prime factorization as sometimes in hurry we make mistakes and then we could not find the results as expected. Also, we have to count while pairing the triplets. Through these things, we can easily solve it.