# CAT Practice : Number System: Factorial

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The following topics are covered in the CAT quant section from Number system - Factorial. Detailed explanatory answers, solution videos and slide decks are also provided.
1. ### Factorial Base 6 base 8 math

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.

1. 22 and 4
2. 32 and 2
3. 24 and 3
4. 25 and 4
24 and 3
• Different bases and factorial
• Hard
2. ### Factorial, factors

Given N is a positive integer less than 31, how many values can n take if (n + 1) is a factor of n!?

1. 18
2. 16
3. 12
4. 20
18
• Factorial, factors, primes
• Hard
3. ### Factorials - basic

How many values can natural number n take, if n! is a multiple of 76 but not 79?

1. 7
2. 21
3. 14
4. 12
4. ### Factorials - basic

How many values can natural number n take, if n! is a multiple of 220 but not 320?

1. 11
2. 21
3. 16
4. 5
5. ### Factorials - Trailing zeroes

How many trailing zeroes (zeroes at the end of the number) does 60! have?

1. 14
2. 12
3. 10
4. 8
6. ### Factorials - basic

What is the highest power of 12 that divides 54!?

1. 25
2. 26
3. 30
4. 4
7. ### Factorials - Trailing zeroes

Find the least number n such that no factorial has n trailing zeroes, or n + 1 trailing zeroes or n + 2 trailing zeroes.

1. 153
2. 126
3. 624
4. 18
8. ### Factorials - base 8

When 40! is expressed in base 8 form, what is the last non–zero digit in the base 8 expansion?

1. 2
2. 6
3. 4
4. 2 or 6
4
• Factorials and octal system
• Hard
9. ### Factorials and Factors

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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