Advertisements
Advertisements
Question
The least number by which 72 be divided to make it a perfect cube is ______.
Advertisements
Solution
The least number by which 72 be divided to make it a perfect cube is 9.
Explanation:
Resolving 72 into prime factors, we get
72 = 2 × 2 × 2 × 3 × 3
Grouping the factors in triplets of equal factors, we get
72 = (2 × 2 × 2) × 3 × 3
Clearly, if we divide 72 by 3 × 3, the quotient would be 2 × 2 × 2, which is a perfect cube.
Hence, the least number by which 72 be divided to make it, a perfect cube, is 9.
APPEARS IN
RELATED QUESTIONS
Find the cube root of the following numbers by the prime factorisation method.
27000
\[\sqrt[3]{125 \times 27} = 3 \times . . .\]
\[\sqrt[3]{} . . . = \sqrt[3]{7} \times \sqrt[3]{8}\]
Evaluate:
Making use of the cube root table, find the cube root
7342 .
With what least number must 8640 be divided so that the quotient is a perfect cube?
Find the smallest number by which 26244 may be divided so that the quotient is a perfect cube.
Find the cube root of 216.
The cube root of 540 × 50 is ___________
The least number by which 72 be multiplied to make it a perfect cube is ______.
