Question

The sum of the digits of the smallest number by which 8748 is to be divided, so that the quotient becomes
a perfect cube is
(A) 2
(B)3
c 6

d) 5
please show steps ​

Answer 1

8748 = 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3 x 3

for it to be perfect cube we need pairs of 3

if we divide by 2 x 2 x 3,

we get 3 x 3 x 3 x 3 x 3 x 3

which is 9 cube

ans = 2 x 2 x 3

= 12

Answer 2

Answer:

The correct answer is option(B) 3

Step-by-step explanation:

Given number is 8748

To find,

The sum of digits of the smallest number by which 8748 is to be divided to get a perfect cube

Solution:

The prime factorization of 8748 is  2 ×2 ×3 ×3 ×3 ×3 ×3 ×3 ×3

It can also be written as  2² ×3⁷

8748 = 3⁷×2²  = 3⁶×3×2²

8748 = (3²)³ ×3×2²

To get a perfect cube (3²)³ ×3×2² should be divided by 3×2²  = 12

$\frac{8748}{12}$ = (3²)³ = 729, is perfect cube

Hence to get a perfect cube, the smallest number by which 8748 is to be divided is = 12

The sum of digit = 1+2 = 3

The sum of digits of the smallest number by which 8748 is to be divided to a get a perfect cube = 3

Hence the correct answer is option(B) 3

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