Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
By what smallest number should we multiply 26244 so that the number becomes a perfect cube? Find the cube root of the number formed.
Given :
The given number is 26244.
To do :
We have to find the smallest number by which 26244 be multiplied to make it a perfect cube.
Solution :
To find the smallest number by which 26244 be multiplied to make it a perfect cube, we have to find the prime factors of it.
Prime factorisation of 26244 is,
$26244 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$
$= (2 \times 2) \times (3 \times 3 \times 3) \times (3 \times 3 \times 3) \times (3 \times 3)$
$ = 2^2 \times 3^3 \times 3^3 \times 3^2 $
As we can see, the given number is a product of 2 square, 3 cubes, 3 cubes, and 3 square. If we multiply the given number by a product of 2 and 3 then it becomes a product of 2 cubes, 3 cubes, 3 cubes, and 3 cubes.
$26244 \times 2 \times 3 = 2^2 \times 3^3 \times 3^3 \times 3^2 \times 2 \times 3$
$26244 \times 6 = 2^3 \times 3^3 \times 3^3 \times 3^3$
$157464 = (2\times 3 \times 3\times 3)^3$.
$157464 = 54^3$.
This implies,
The cube root of 157464 is 54.
Therefore, the smallest number that has to be multiplied to make 26244 a perfect cube is 6 and the cube root of 154764 is 54.
487 Views
