The value of 50! is the product of all the whole numbers from 1 to 50 inclusive, i.e. 50! = 1x2x3x...x49x50. Find the maximum number of divisions...

I assume we are asked to find the maximum number of times we can divide 50! by 2 and still get an integer, or how many times is 50! evenly divisible by 2:

This is equivalent to asking how many 2's are in the prime factorization of 50!.

There are 25 even terms each contributing a 2.There are 12 terms that are multiples of 4 contributing another 2.There are 6 terms that are...

I assume we are asked to find the maximum number of times we can divide 50! by 2 and still get an integer, or how many times is 50! evenly divisible by 2:

This is equivalent to asking how many 2's are in the prime factorization of 50!.

There are 25 even terms each contributing a 2.
There are 12 terms that are multiples of 4 contributing another 2.
There are 6 terms that are multiples of 8 contributing another 2.
There are 3 terms that are multiples of 16 that contribute another 2.
There is 1 term that is a factor of 32 contributing another 2.

Thus there are 25+12+6+3+1=47 2's in the prime factorization of 50! so we can evenly divide by 2 47 times.