CAT Quantitative Aptitude Questions | CAT Number Systems - Factorial questions

The question is about Factorials and octal system. Given a factorial x!, we need to find out the last non-zero digit when the number is expressed in octal system. A range of CAT questions can be asked based on this simple concept of CAT Number Systems in the CAT exam. Factorials is also helpful in Permutation and Combination questions for the CAT Exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz,head on here to take these questions in a test format, absolutely free.

Question 8: When 40! is expressed in base 8 form, what is the last non–zero digit in the base 8 expansion?

1. 2
2. 6
3. 4
4. 2 or 6

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Number Theory - Factorial: A number in base 8 that ends in 4 is a multiple of 4 but not 8. If you 'get' this idea, this question should be easy

We need to find the largest power of 8 that divides 40!.
We need to find the largest power of 2 that divides 40!
This is given by (\\frac{40}{2}\\)) and then successive division by 2. = 20 + 10 + 5 + 2 + 1 = 38

So, 2³⁸ divides 40! Or, (2³)¹² * 2² divides 40!

(2³)¹² divides the number, or the base 8 representation ends with 12 zeroes. Now, the base 8 representation of this number will be some (abcd…n)₈ * (1000000000000)₈. Now, (abcd…n)₈ does not end in 0 and is a multiple of 2². The last digit has to be 4.

The last non–zero digit is 4.

The question is "what is the last non–zero digit in the base 8 expansion?"

Hence the answer is "4"

Choice C is the correct answer.