A CAT Number theory question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Factors, Factorials, HCF and LCM, Base System & Remainders. In CAT Exam, one can generally expect a few questions from CAT Number Systems. CAT Number Systems is an important topic in the CAT Exam. Inside this vast topic, Factorials is tested frequently. You can expect approx 1 question involving CAT factorials. As an aside, Factorials is also useful in CAT Permutation and Combination. 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.
A number n! is written in base 6 and base 8 notation. Its base 6 representation ends with 10 zeroes. Its base 8 representation ends with 7 zeroes. Find the smallest n that satisfies these conditions. Also find the number of values of n that will satisfy these conditions.
Given N is a positive integer less than 31, how many values can n take if (n + 1) is a factor of n!?
How many values can natural number n take, if n! is a multiple of 7^{6} but not 7^{9}?
How many values can natural number n take, if n! is a multiple of 2^{20} but not 3^{20}?
How many trailing zeroes (zeroes at the end of the number) does 60! have?
What is the highest power of 12 that divides 54!?
Find the least number n such that no factorial has n trailing zeroes, or n + 1 trailing zeroes or n + 2 trailing zeroes.
When 40! is expressed in base 8 form, what is the last non–zero digit in the base 8 expansion?
Let K be the largest number with exactly 3 factors that divide 25! How many factors does (k – 1) have?
The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.
For some natural number \(n\), assume that \((15,000)\) ! is divisible by \((n !) !\). The largest possible value of \(n\) is
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