what's the minimum slices does it needs to slice a cube into $1100$ equal parts?

Question

I have tried using prime factorization which is $2^2 \times 5^2 \times 11$ and found out that I'll need $37$ slices. but in the question paper which is a multiple choice question there's no such answer. the choices are $30,31,32,61,110$.

Answer 1

To split the cube into $10 \times 10 \times 11$ equal parts as suggested by @bof, you need $9 + 9 + 10 = 28$ cuts. This separates the original cube in $10 + 10 + 11 = 31$ slices.

However, you can bring down this number to $5 + 4 + 4 = 13$ cuts by stacking the intermediate slabs and thus yielding more parts per cut.

The following picture illustrates how to get $11$ slices with five cuts:

Similarly, $10$ slices can be obtained with four cuts:

Answer 2

You are asked to count the slices, not the cuts.

Hence with $10\times10\times11=1100$,$$10+10+11=31.$$