Question

8019,Find the smallest number by which the given number must be divided to obtain a perfect cube.

Answer 1

Hey !!

Given,

Number = 8019

The prime factorization of 8019 is,

8019 = 3 × 3 × 3 × 3 × 3 × 3 × 11

Here, 11 is extra factor of 8019 Hence we should divide 8019 by 11. The answer is 729

Prime factorization of 729 is,

1000 = 3 × 3 × 3 × 3 × 3 × 3

All the numbers are group into 3. Hence, the cube root of 8019 is 9.

Answer 2

HELLO FRIEND HERE IS YOUR ANSWER,,,,,,

The given number or value here , is ; "8019"

By the method of prime factorisation , that is , Prime numbers of this value or number ;

$= > 8019 = > 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 11$

Now , The group of three numbers are "3" and "3" , 11 is not a group unlike the other two factors (in group) , so , the number is not a perfect cube , therefore , in order to get a perfect cube the account of an extra prime factor is taken , 8019 is divisible by 11 which obtains us the value of,,,

$= > \frac{8019}{11} \\ \\ = > 729$
Again by the method of finding the prime numbers or prime factors by the method of Prime factorisation,,,,

$= > 729 = > 3 \times 3 \times 3 \times 3 \times 3 \times 3$
By grouping the given three pairs (3) and (3) . The perfect cube we get here is,,,,

$= > {(3)}^{3} \times {(3)}^{3} \\ \\ = > 3 \times 3 \\ \\ = > 9$
Therefore ,, the perfect cube we get here for the number or value "8019" is $\textbf{"9"}$.

HOPE IT HELPS YOU AND CEDARS YOUR DOUBTS FOR PERFECT CUBES!!!!!!