### 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.

- 22 and 4
- 32 and 2
- 24 and 3
- 25 and 4

**Correct Answer**Choice (C).

24 and 3 Correct answer- Explanatory Answer
- Different bases and factorial
- Hard

### 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!?

- 18
- 16
- 12
- 20

**Correct Answer**Choice (A).

18 Correct answer- Explanatory Answer
- Factorial, factors, primes
- Hard

### Factorials - basic

How many values can natural number n take, if n! is a multiple of 7

^{6}but not 7^{9}?- 7
- 21
- 14
- 12

**Correct Answer**Choice (C).

14 Correct answer- Explanatory Answer
- Factorials - basic
- Medium

### Factorials - basic

How many values can natural number n take, if n! is a multiple of 2

^{20}but not 3^{20}?- 11
- 21
- 16
- 5

**Correct Answer**Choice(B).

21 Correct answer- Explanatory Answer
- Factorials - basic
- Medium

### Factorials - Trailing zeroes

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

- 14
- 12
- 10
- 8

**Correct Answer**Choice (A).

14 Correct answer- Explanatory Answer
- Trailing zeroes
- Medium

### Factorials - basic

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

- 25
- 26
- 30
- 4

**Correct Answer**Choice (A).

25 Correct answer- Explanatory Answer
- Factorials - basic
- Hard

### 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.

- 153
- 126
- 624
- 18

**Correct Answer**Choice (A).

153 Correct answer- Explanatory Answer
- Trailing zeroes
- Hard

### Factorials - base 8

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

- 2
- 6
- 4
- 2 or 6

**Correct Answer**Choice (C).

4 Correct answer- Explanatory Answer
- Factorials and octal system
- Hard

### Factorials and Factors

Let K be the largest number with exactly 3 factors that divide 25! How many factors does (k – 1) have?

- 16
- 12
- 9
- 14

**Correct Answer**Choice (A).

16 Correct answer- Explanatory Answer
- Factorials and Factors
- Hard

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