Question

7000,Find the smallest number by which the given number must be divided to obtain a perfect cube.

Answer 1

Hey !!

Given,

Number = 7000

The prime factorization of 7000 is,

7000 = 2 × 2 × 2 × 5 × 5 × 5 × 7

Here, 7 is extra factor of 7000. Hence we should divide 7000 by 7. The answer is 1000

Prime factorization of 1000 is,

1000 = 2 × 2 × 2 × 5 × 5 × 5

All the numbers are paired in 3. The cube root of 1000 is 10.

Answer 2

HELLO FRIEND HERE IS YOUR ANSWER,,,,,

The given number or value here, is ; "7000"

By the method of prime factorisation, that is , Prime numbers of this value or number "7000"

$= > 7000 = > 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 7$

Now , The group of three numbers are "2" and "5" , 7 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 , 7000 is divisible by 7 which obtains us the value of,,,

$= > \frac{7000}{7} \\ \\ = > 1000$
Again , by the method of finding the prime factors by Prime factorisation ,,,,

$= > 1000 = > 2 \times 2 \times 2 \times 5 \times 5 \times 5$
By grouping the three pairs (2) and (5). The perfect cube number for 7000 is "10".

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