FREE! Click here to Join FunTrivia. Thousands of games, quizzes, and lots more!

Factorial! Trivia Quiz

The factorial operations come in useful in many mathematics areas, especially in the calculations of combinations and permutations. How much do you know about them?

A multiple-choice quiz by Matthew_07. Estimated time: 6 mins.

Author
Matthew_07

Time
6 mins

Type
Multiple Choice

Quiz #
273,626

Updated
Dec 03 21

# Qns
10

Difficulty
Difficult

Avg Score
5 / 10

Plays
570

Question 1 of 10

1. The factorial of an integer n is denoted by n!. This n! notation was first used by a French mathematician. Who was he? Hint

Leonhard Euler

Sophie Germain

Pierre de Fermat

Christian Kramp

NEXT>

Question 2 of 10

2. Since n! = n x (n-1) x (n-2) x ... x 1, then n! can also be written as n(n-1)!. So, what is the value of (100!)/( 99!) ?

Answer: (An integer (a numeric value))

NEXT>

Question 3 of 10

3. We know that n! = n(n-1)(n-2)...(1). For example, 4! = 4 x 3 x 2 x 1 = 24. But what does the double factorial of 4, namely 4!! represent? Hint

4 x 2

(24/4)! = 6!

24 x 23 x 22 x ... x 1

(24 x 4)! = 96 x 95 x 94 x ... x 1

4. Given that n! = n(n-1)(n-2)...(2)(1). Instead of multiplication, there exists an analog series that is defined by addition, that is, f(n) = n + (n-1) + (n-2) + ... + 2 + 1. This type of number is known as a/an? Hint

Archimedes number

Perfect number

Triangular number

Magic number

NEXT>

Question 5 of 10

5. A typical scientific calculator can calculate the value for the factorials up to 69!, but the value for 70! is greater than 10^100. Which of the following approximations is used to calculate the approximation for large factorials? Hint

Nernst's approximation

Taylor's approximation

Stirling's approximation

Maclaurin's approximation

NEXT>

Question 6 of 10

6. A positive integer that is in the form of n^(n-1)^[(n-2)^...^2^(1)] is called a/an ? Hint

Power factorial

Exponential factorial

Infinite factorial

Logarithm factorial

NEXT>

Question 7 of 10

7. A prime number that is 1 more or 1 less than the value of a factorial is called a factorial prime. Which of the following numbers is not a factorial prime? Hint

3! - 1 = 5

5! - 1 = 119

4! - 1 = 23

6! - 1 = 719

NEXT>

Question 8 of 10

8. Factorial operations are used widely in combinations and permutations problems. To find the number of different ways one can select r items from a total of n items, we use the combination formula, which is n C r = (n!)/[(n-r)!](r!). On the other hand, the formula for permutation, given by n P r, is? Hint

r!/n!

n!/r!

n!/(n-r)!

(n-r)!/n!

NEXT>

Question 9 of 10

9. Factorials also come in useful in calculus. Some exponential and trigonometry functions can be expressed as a power series of x, as what is stated and defined in which of the following theorems? Hint

Polynomial's theorem

Gauss' theorem

Cayley-Hamilton's theorem

Taylor's theorem

NEXT>

Question 10 of 10

10. The factorial of 0, namely 0! is 0.

True

False

(Optional) Create a Free FunTrivia ID to save the points you are about to earn:

Select a User ID:

Choose a Password:

Your Email:

Quiz Answer Key and Fun Facts

1. The factorial of an integer n is denoted by n!. This n! notation was first used by a French mathematician. Who was he?

Answer: Christian Kramp

Kramp was born in Strasbourg, France in 1760. He used the notation n! in 1808 in one of his books, "Elements d'arithm�tique Universelle".

2. Since n! = n x (n-1) x (n-2) x ... x 1, then n! can also be written as n(n-1)!. So, what is the value of (100!)/( 99!) ?

Answer: 100

Notice that 100! = 100 (99!). Hence, (100!)/(99!) = [100(99!)]/(99!) The 99! cancels out and the 100 remains.

3. We know that n! = n(n-1)(n-2)...(1). For example, 4! = 4 x 3 x 2 x 1 = 24. But what does the double factorial of 4, namely 4!! represent?

Answer: 4 x 2

Note: n|| means the double factorial of n.

If n equals or greater than 2, then n|| = n(n-2)||. For example, 10! = 10 x 8 x 6 x 4 x 2. Another example involving an odd number would be 13! = 13 x 11 x 9 x 7 x 5 x 3 x 1.

An interesting identity that can be derived from here is n! = n||(n-1)||. For instance, we take the value of n = 3. So, on the left hand side, we have 3! = 3 x 2 x 1 =6. On the right hand side, we have (3||) x (2||) = (3 x 1) x (2) = 6.

We should keep in mind that the double factorial, n|| is not equal to the nested factorial, (n|)|. For example, for the double factorial of 4, it would be 4 x 2 = 8. But the nested factorial of 4 is given by (4|)| = 24!.

Answer: Triangular number

The first triangular number is 1. The second one is 2 + (2-1) = 2 + 1 = 3. The third triangular number is given by 3 + (3-1) + (3-2) = 3 + 2 + 1 = 6. This is followed by 10, 15, 21.
Another simpler way to calculate the nth triangular number would be by using the formula [(n)(n+1)]/2. For instance, the 5th triangular number is [(5)(6)]/2 = 15.

Answer: Stirling's approximation

Stirling's approximation, also known as Stirling's formula, is named after James Stirling. The formula is given by n! approaches [{surd (2pi x n)}{n^n}]/{e^n}.

For example, the value of 50! is 3.0414 x 10^64. By substituting n = 50, we obtain 50! = 3.0363 x 10^64, which is very close to its real value.

6. A positive integer that is in the form of n^{(n-1)^[(n-2)^...^{2^(1)}]} is called a/an ?

Answer: Exponential factorial

Let f(n) be the exponential factorial function for an integer n.
When n = 1, f(n) = 1
When n = 2, f(n) = 2^1 = 2
When n = 3, f(n) = 3^(2^1) = 9
When n = 4, f(n) = 4^[3^(2^1)] = 262144

It should be noticed that when calculating the exponential factorial for n = 4, the operation involved is 4^[3^(2^1)], not [(4^3)^2]^1

7. A prime number that is 1 more or 1 less than the value of a factorial is called a factorial prime. Which of the following numbers is not a factorial prime?

Answer: 5! - 1 = 119

119 is the product of 2 smaller primes, which are 7 and 17. Some other factorial primes are such as 1! + 1 = 2, 2! + 1 = 3, 3! + 1 = 7.

8. Factorial operations are used widely in combinations and permutations problems. To find the number of different ways one can select r items from a total of n items, we use the combination formula, which is n C r = (n!)/{[(n-r)!](r!)}. On the other hand, the formula for permutation, given by n P r, is?

Answer: n!/(n-r)!

For permutation, we wish to find the number of different ways one can arrange r items in different orders, selected from a total of n items.

Answer: Taylor's theorem

Some of the famous power series that is derived from this Taylor's theorem is cos x = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + (x^8)/8! -... Apart from this, the functions sin x, tan x, and e^x can also be expressed as power series.

10. The factorial of 0, namely 0! is 0.

Answer: False

Actually, 0! = 1. We notice the followings:
1! = 1
2!= 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
5! = 5 x 4 x 3 x 2 x 1 = 120

Working backwards, we will get:
4! = 5!/5 = 24
3! = 4!/4 = 6
2! = 3!/3 = 2
1! = 2!/2 = 1
0! = 1!/1 = 1

Therefore, the operation of 5 C 0 is valid and possible, where the answer is 1. This means that we have only 1 way of choosing 0 items from a total of 5 items.

Source: Author Matthew_07

This quiz was reviewed by FunTrivia editor crisw before going online.
Any errors found in FunTrivia content are routinely corrected through our feedback system.