CAT Exam Model Paper 5 with solutions for free online practice

Using prime factorization:
$2700=2^2{.3}^3{.5}^2$
$=2\times 2\times 3\times 3\times 3\times 5\times 5\times 1$ (8 integers)
Clearly if 2700 has to be written as product of 8 distinct integers, some of those have to be negative.
$2700=3\times 2\times \left(-2\right)\times 3\times \left(-3\right)\times 5\times \left(-5\right)\times 1\times \left(-1\right)$
3 can be multiplied to any one out of the 8 integers inside the bracket except 1 and - 1 otherwise we'll have two 3’s or two - 3’s.
Hence, 6 ways are possible.