# CAT Quantitative Aptitude Questions | CAT Number Systems - Factorial questions

###### CAT Questions | Number Theory | Factorials and Factors CAT Questions

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

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2020Online Batches Available Now!

##### 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.

###### CAT Coaching in ChennaiCAT 2020Enroll at 35,000/-

Online Classroom Batches Starting Now!

###### Best CAT Coaching in ChennaiRegister Online, get Rs 7000/- off

Attend a Demo Class

## CAT Online Coaching | CAT Number Systems questions Videos On YouTube

#### Other useful sources for Number System Questions | Number Theory Factorials Sample Questions

##### Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

##### How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com