Question

1536,Find the smallest number by which the given number must be divided to obtain a perfect cube.

Answer 1

Hey !!

Given,

Number = 1536

The prime factorization of 1536 is,

1536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

Here, 3 is extra factor of 1536 Hence we should divide 1536 by 3. The answer is 512

Prime factorization of 512 is,

1000 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

All the numbers are group into 3. Hence, the cube root of 1536 is 8.

Answer 2

HELLO FRIEND HERE IS YOUR ANSWER,,,,,

The given number or valuer here , is ; "1536"

By the method of prime factorisation , that is , Prime factors of this particular value "1536" ,,

$= > 1536 = > 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$

Now , The group of three numbers are "2" , "2" and "2" , 3 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 , 1536 is divisible by 3 which obtains us the value of,,,

$= > \frac{1536}{3} \\ \\ = > 512$
Again , by the method of finding prime numbers or prime factors by the given process of prime factorisation , we get ,,,

$= > 512 = > 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
By grouping the given terms present in the prime factorisation of the value "512" (2) , (2) and (2). The perfect cube of the value or number "1536" , is ,,,

$= > {(2)}^{3} \times {(2)}^{3} \times {(2)}^{3} \\ \\ = > 2 \times 2 \times 2 \\ \\ = > 8$
Therefore, after the collective mash up between the numbers of "2" . We get the perfect cube for "1536" as "8" .

Which is the required solution for this question .

HOPE THIS HELPS YOU AND CLEARS YOUR DOUBTS FOR PERFECT CUBES!!!!!