Question

It's URGENT!!!

Find the smallest number by which 16384 be divided so that the quotient may be a perfect cube​

Answer 1

ANSWER:-

NOW,IF WE DIVIDE 16384=2×2×2×2×2×2×2×2×2×2×2×2×2

=(2×2×2)

(2×2×2)×(2×2×2)×(2×2×2)×2×2.

IF WE DIVIDE 16384 BY 2×2=4 THEN THE QUOTIENT OBTAINED IS 4096 WHICH IS A PERFECT CUBE.

HENCE,SMALLEST NUMBER REQUIRED IS 16.

Answer 2

$\: \: \: \: \: 2 |16384| \\ \: \: \: \: \: \:2 |8192| \\ \: \: \: \: \: \: 2 |4096| \\ \: \: \: \: \: \: 2|2048| \\ \: \: \: \: \: \: 2|1024| \\ \: \: \: \: \: \: 2|512| \\ \: \: \: \: \: \: 2 |256| \\ \: \: \: \: \: \: 2 |128| \\ \: \: \: \: \: \: 2|64| \\ \: \: \: \: \: \: 2 |32| \\ \: \: \: \: \: \: 2 |16| \\ \: \: \: \: \: \: \: 2 |8| \\ \: \: \: \: \: \: 2|4| \\ \: \: \: \: \: \: 2 |2| \\ \: \: \: \: \: \: \: \: |1| \\ 1638 = (2 \times 2 \times 2) \times (2 \times 2 \times 2) \\ \: \: \: (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times 2 \\ \: \: \: \: \times 2 \\so \: when \: we \: divide \: by \: 4 \: then \: quotient \: will \: be \: a \: perfect \: cube.$
hence the required
smallest number =4