Find the smallest natural number by which 30184 must be divided so that the quotient is a perfect cube.<br />
Answers
Answered by
3
The smallest natural number by which 30184 must be divided so that the quotient is a perfect cube is 11.
- Natural numbers are all numbers which are positive and whole numbers.Sometimes zero is also counted as a natural number.
- So, when 30184 is divided by 11, which is a natural number, it gives the quotient as 2744.
- Perfect cubes are the numbers which are the perfect multiplication of a specific number, three times.
- Therefore, 2744 = 14 * 14 * 14. So, 2744 is a perfect cube.
Answered by
2
The smallest natural number divided by 30184 is 11
Explanation:
The prime factors of the given number is:
30184 = 2, 2, 2, 7, 7, 7, 11
⇒ 30184 = 2³ × 7³ × 11
30184/11 = 2³ × 7³
2744 = 2³ × 7³
∴ 2744 = 14 × 14 × 14
Thus, when 30184 is divided by 11, we get 2744 which is a prefect cube of 14.
Similar questions