Questions tagged [factorial]

This tag is for challenges involving the factorial of a number, the product of the numbers from 1 to n

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8 votes
7 answers
534 views

Factorials of primes decomposition

You have to decompose a positive integer/fraction as a product of powers of factorials of prime numbers. For example ...
  • 3,219
18 votes
3 answers
602 views

Find a factorial with n trailing zeros, quickly

Problem A fact you may have noticed about factorials is that as \$n\$ gets larger \$n!\$ will have an increasing number of \$0\$s at the end of it's base \$10\$ representation. In fact this is true ...
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4 votes
1 answer
220 views

Calculate the (n x "super")factorial [duplicate]

Introduction Factorials are one of the most frequently used examples to show how a programming language works. A factorial, denoted \$n!\$, is \$1⋅2⋅3⋅…⋅(n-2)⋅(n-1)⋅n\$. There is also the ...
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20 votes
21 answers
3k views

Implement the Torian

The Torian, \$x!x\$, of a non-negative integer \$x\$ can be recursively defined as $$ x!0 = x \\ x!n = \prod^x_{i=1} i!(n-1) = 1!(n-1) \times 2!(n-1) \times \cdots \times x!(n-1) $$ The Torian is then ...
20 votes
9 answers
614 views

Zeroes at end of \$n!\$ in base \$m\$

Related: Zeroes at the end of a factorial Today, we are going to calculate how many zeroes are there at the end of \$n!\$ (the factorial of \$n\$) in base \$m\$. Or in other words: For given integers \...
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46 votes
121 answers
7k views

The vanilla factorial challenge

Task Given a non-negative integer \$n\$, evaluate the factorial \$n!\$. The factorial is defined as follows: $$ n!=\begin{cases}1 & n=0\\n\times(n-1)!&n>0\end{cases} $$ Rules All default I/...
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20 votes
9 answers
650 views

Prime Modified Z-Factorials

Let me explain one by one the above terms... We will call \$\text{Z-Factorial}(n)\$ of a positive integer \$n\$, \$n!\$ (i.e. \$n\$ factorial) without any trailing zeros. So, \$\text{Z-Factorial}(30)\$...
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21 votes
37 answers
3k views

Reverse factorial function

Given a number n, find x such that x! = n, where both x and n are positive integers. Assume the input n will always be the factorial of a positive integer, so something like n=23 will not be given as ...
35 votes
18 answers
6k views

Bad factorial joke

Sometimes I make bad jokes... And a bad joke I like to make involves interpreting exclamation marks in sentences as the factorial sign. Task Your task is to write a program that receives a sentence ...
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38 votes
40 answers
6k views

Repeated! Factorials!

Not to be confused with Find the factorial! Introduction The factorial of an integer n can be calculated by $$n!=n\times(n-1)\times(n-2)\times(...)\times2\times1$$...
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32 votes
21 answers
2k views

A ​Note ​on ​N!

J. E. Maxfield proved following theorem (see DOI: 10.2307/2688966): If \$A\$ is any positive integer having \$m\$ digits, there exists a positive integer \$N\$ such that the first \$m\$ digits of \$N!...
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1 vote
3 answers
795 views

Finding Factorials with Gamma [duplicate]

Introduction We know that the factorial notation is valid for all natural numbers. However, Euler had extended it for all positive real numbers, as well as for complex numbers by defining a function, ...
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16 votes
5 answers
928 views

Factoring factorials

Today in my statistics class, I found that some factorials can be simplified when multiplied together! For example: 5! * 3! = 5! *3*2 = 5! *6 = 6! Your job: Given ...
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17 votes
21 answers
2k views

Additional facts!

In mathematics, the factorial, shortened "fact" of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! is 1 * 2 * 3 * 4 * 5 = 120 ...
12 votes
7 answers
742 views

Do two numbers contain unique factorials?

Break two numbers up into their factorials; if they share any, return a falsey value. Otherwise, return a truthy value. (inspired by this recent question) In other words, write each input number as ...
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37 votes
30 answers
4k views

Factorials and never ending cycles!

As you may know it, the factorial of a positive integer n is the product of all the positive integers which are equal or smaller to ...
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192 votes
61 answers
30k views

Mathematics is fact. Programming is not

In mathematics an exclamation mark ! often means factorial and it comes after the argument. In programming an exclamation mark ! ...
25 votes
38 answers
4k views

Big numbers: Ultrafactorials

Ultrafactorials The ultrafactorials are a sequence of numbers which can be generated using the following function: $$a(n) = n! ^ {n!}$$ The resulting values rise extremely quickly. Side note: This is ...
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27 votes
53 answers
5k views

Factorial digit sum

The challenge is to calculate the digit sum of the factorial of a number. Example Input: 10 Output: 27 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800, and the sum of ...
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40 votes
30 answers
3k views

Pseudofactorial

There is a rather curious number which shows up sometimes in math problems or riddles. The pseudofactorial(N) is the least (i.e. lowest) common multiple of the numbers 1 through N; in other words, it'...
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40 votes
61 answers
6k views

Zeroes at the end of a factorial

Write a program or function that finds the number of zeroes at the end of n! in base 10, where n is an input number (in any ...
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22 votes
10 answers
1k views

Last Nonzero Digits of a Factorial in Base

You should write a program or function which given three positive integers n b k as input outputs or returns the last k digits ...
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1 vote
4 answers
724 views

Memory is Expensive [closed]

You are a robot. You are stranded in a small cage with weird humans wearing weird suits looking at you. Your solar panel is malfunctioning, and your energy is running out. On the wall there is a ...
14 votes
16 answers
7k views

How much can you quickly multiply?

With the recent Python bashing, here's an attempt to show Python's strengths. Your challenge is to write a program that calculates the factorial of as high a number ...
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31 votes
9 answers
4k views

Calculate the inverse of factorial

Write the shortest code that will take any real number greater than 1 as input and will output its positive inverse factorial. In other words, it answers the question "what number factorial is equal ...
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24 votes
17 answers
5k views

Last non-zero digit of n!

Given an integer 1 ≤ N ≤ 1,000,000 as input, output the last non-zero digit of N!, where ! is the factorial (the product of all numbers from 1 to N, inclusive). This is OEIS sequence A008904. Your ...
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89 votes
207 answers
20k views

Find the Factorial!

Create the shortest program or function that finds the factorial of a non-negative integer. The factorial, represented with ! is defined as such $$n!:=\begin{...