Find the least natural number by which 2160 should be divided so that the quotient is a perfect cube . also find cube of quotient
Answers
2160/2*5
2160/10
³√216=6
SO ANSWER IS 6//
The least natural number is 10, which after division leave 2160 as perfect cube number and .
Step-by-step explanation:
Given:
- A number.
To find:
- Find the least natural number by which 2160 should be divided so that the quotient is a perfect cube .
- Also find cube root of quotient.
Solution:
Concept to be used:
- Do prime factorization of number.
- Make set of 3 same prime numbers.
- Take the numbers separately, which can not make pairs of three.
Step 1:
Do prime factorization of 2160.
Step 2:
Make pairs of 3 same prime factors.
Step 3:
Find the least number for division.
As,
2 and 5 are separate from pairs.
Thus,
The least number is 10, by which 2160 is divided to get a perfect cube number.
Step 4:
Find the cube root of quotient.
On dividing 2160 with 10, we get 216 as quotient.
So,
or
or
or
Thus,
The least natural number is 10, which after division leave 2160 as perfect cube number and cube root of 216 is 6.
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