CAT Quantitative Aptitude Questions | CAT Number Systems - Factorial questions

CAT Questions | Number Theory | Factorials and Factors

The question is about Factorials and Factors. We need to find 'K' such that it satisfies the following condition and theen the number of factors of 'K-1'. Dealing with factorials of a number is a vital component in CAT Number Theory. A range of CAT questions can be asked based on this simple concept. 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 9: Let K be the largest number with exactly 3 factors that divide 25! How many factors does (k – 1) have?

  1. 16
  2. 12
  3. 9
  4. 14

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Explanatory Answer

Method of solving this CAT Question from Number Theory - Factorial: A number with exactly 3 factors - what type of number is this? Key question that you must know the answer to.

A number with exactly 3 factors has to be square of a prime.
Now, 32 divides 25! So do 52, 72, 112.
132 will not divide 25!
So the largest number with 3 factors that divide 25! is 121.
K – 1 = 120 = 23 * 3 * 5
K – 1 has 16 factors.

The question is "How many factors does (k – 1) have?"

Hence the answer is "16"

Choice A is the correct answer.

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