Question

Find the least number by which 16384 must be divided ,so that the quotient is a perfect cube

Answer 1

Firstly find out the prime factorisation
of 16384
2|16384
2|8192
2|4096
2|2048
2|1024
3|512
2|256
2|128
2|64
2|32
2|16
2|8
2|4
2|2
By prime factorisation we get,
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)
(2×2)
so,to make it a prefect cube it must be divided by 4.