Factorials Test
Number of questions:10
Q.1 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.
Q.2 Given N is a positive integer less than 31, how many values can n take if (n + 1) is a factor of n!?
Q.3 How many values can natural number n take, if n! is a multiple of 76, but not 79,?
Q.4 How many values can natural number n take, if n! is a multiple of 220, but not 320?
Q.5 How many trailing zeroes (zeroes at the end of the number) does 60! have?
Q.6 What is the highest power of 12 that divides 54!?
Q.7 Find the least number n such that no factorial has n trailing zeroes, or n + 1 trailing zeroes or n + 2 trailing zeroes.
Q.8 When 40! is expressed in base 8 form, what is the last non–zero digit in the base 8 expansion?
Q.9 Let K be the largest number with exactly 3 factors that divide 25! How many factors does (k – 1) have?
Q.10 The maximum value of the natural number n for which 21n, divides 50! is?
