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?

- 2
- 6
- 4
- 2 or 6

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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, 2^{38} divides 40! Or, (2^{3})^{12} * 2^{2} divides 40!

(2^{3})^{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 2^{2}. 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?"**

Choice C is the correct answer.

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