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r/math on Reddit: Interesting phenomenon with 10 factorial

August 7, 2023 -

I saw a post on this sub a few days ago (sorry, I tried to find it with no luck) where someone pointed out that: 1*2*3*4*5*6*7*8*9*10 = 1*2*3*4*5*6*7*6*5*4*3*2*1 It makes sense because the first 1 through 7 cancel out, then the prime factorization of 8*9*10 (2⁴ * 3²\ * 5) matches that for 1-6.

My question is: are there other examples of this? To formalize, for any two real number m and n, such that m<n, how many examples are there where n! = m! * (m+1)! (The above example of course being m=6 and n=10)

My gut intuition is that it would have to be during a decent length string of composite numbers.

Poor man used * for multiplication and it became italics

Type 1\*2\*3\*4 to stop multiplication from becoming italics

product of all integers between 1 and the integral input of the function

In mathematics, the factorial of a non-negative integer ... {\displaystyle {\begin{aligned}n!&=n\times (n-1)\times (n-2)\times (n-3)\times \cdots \times 3\times 2\times 1\\&={\begin{cases}1,&{\text{if }}n=0\\n\times (n-1)!,&{\text{if }}n\geq 1.\end{cases}}\\\end{aligned}}} For example, ... ... … Wikipedia

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Factorial - Wikipedia

1 week ago - An elementary proof of Bertrand's postulate on the existence of a prime in any interval of the form ... {\displaystyle [n,2n]} , one of the first results of Paul Erdős, was based on the divisibility properties of factorials. The factorial number system is a mixed radix notation for numbers in which the place values of each digit are factorials.

History Definition Applications Properties Related sequences and functions

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People also ask

What is a factorial of 0?

The value of factorial of 0 is 1, i.e. 0! = 1.

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What is the symbol of factorial?

The factorial function is a mathematical formula represented by an exclamation mark “!”. For example, the factorial of 8 can be represented as 8! and it is read as eight factorial.

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What is the meaning of 5 factorial?

The meaning of 5 factorial is that we need to multiply the numbers from 1 to 5. That means, 5! = 5 × 4 × 3 × 2 × 1 = 120.

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Factorial - Meaning, Formula | Factorial of Hundred & 0

Factorial in math is one of the ... examples of factorial of numbers. 8 factorial = 8! = 8 · 7 · 6 ·5 · 4 · 3 · 2 · 1 = 40,320 · 10 factorial = 10!...

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What is the factorial of 10 class 12 maths CBSE

Hint: The factorial of 10 can also be written as 10!. To find a factorial of a number, you need to find the product of all the numbers up to that number. Suppose if you need to find the factorial of the number 5 you need to multiply all the numbers up to 5 that is 1, 2, 3, 4, 5. Therefore, to get the factorial of 10, you need to multiply all the numbers up to 10 that is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.Complete step by step solution:Here is the step wise solution.First we need to know what a factorial is. To find a factorial of a number, we need to find the product of all the numbers up to that number. Suppose, if we need to find the factorial of 4, we need to multiply all the numbers up to 4. The numbers up to 4 are 1, 2, 3, and 4. Therefore, multiplying the, we get 24. Therefore, the factorial of 4 is 24.In the question, we are asked to find the factorial of 10. Therefore, we multiply all the numbers up to 10, that is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.Therefore, we get the factorial of 10 as 3628800.Note: You need to remember what a factorial is. It is very important in the topic of permutations and combinations. To find a factorial you could also use the stirling's approximation. Also it would be easy, if you remember the factorials for numbers till 10.

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Factorial Calculator n!

You may want to copy the long integer answer result and paste it into another document to view it. n! = n × (n - 1) × (n - 2) × (n - 3) × ... × 1 · Factorial of 10 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800 ... A ...

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Visit BYJU’S – The Learning App for more information on factorial of numbers and explore Maths-related videos to learn with ease. ... The value of factorial of 10 is 3628800, i.e.

Published October 6, 2021

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What is the factorial of 10? - Factorial Calculator

If n is a natural number greater than or equal to 1, then · n! = n x (n - 1) x (n - 2) x (n - 3) ... 3 x 2 x 1 · If n = 0, then n! = 1, by convention. ... Trailing zeros are a sequence of zeros in the decimal representation of a number, after which no other digits follow. This video shows how to find the trailing zeros of a factorial easily. 10!

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Factorial Function !

So 10! = 10 × 9!, ... and 125! = 125 × 124!, and so on. Zero Factorial is interesting ... it is generally agreed that 0! = 1. It may seem funny that multiplying no numbers together results in 1, but let's follow the pattern backwards from, say, 4!

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What is the factorial of 10 ? - askIITians

July 16, 2025 - The factorial of a number is a fundamental concept in mathematics, particularly in combinatorics and algebra. When we talk about the factorial of 10, we denote it as 10!. This notation represents the product of all positive integers from 1 up to 10.

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10! - Factorial of 10

Enter an integer 0-50,000. The calculator will compute the factorial and the number of digits it contains. A factorial of N is the product of all positive integers between 1 and N inclusive. For example, the factorial of 5 is 5×4×3×2×1=120. The one exception is 0!, which is defined as 1.

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What is the Factorial of 10? | 10 Factorial [Solved]

October 8, 2025 - Therefore, the factorial of 10 is 3,628,800. Factorial: The way of multiplying all the natural numbers smaller than the original number is known as factorial, and it is expressed with an exclamation mark (!).

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Factorial – Definition, Notation, Formula, Properties & Examples | Testbook

The notation n! pronounced "n factorial " is a short hand form for repeated multiplication that Christian Kramp introduced in 1808. Here n denotes the main valuea whole number 0 or greaterand the exclamation point shows the operation of n being multiplied by n 1 n 2 etc. down to 1. This brief notation enables mathematicians to describe huge numbers and complicated product sequences in a very concise manner. So the expression 10!

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Factorial Calculator

The Factorial Calculator can compute a factorial for any number up to 10,000. Beyond 10,000, the calculator reports a lower-bound estimate. Here's the logic. The value of 10,000! is approximately 2.846 x 1035659. Therefore, we know the factorial of any integer greater than 10,000 will be at ...

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What is the factorial 10 number in a for loop? - Quora

Answer (1 of 2): You create a variable for the product. This variable is initially equal to 1. (Why 1? - because 1 is the identity element of multiplication. For addition, you would use 0 instead, and for the same reason.) Then, you write a loop where the loop variable takes on all the values fr...

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Factorial: Meaning, Formula, Values for Numbers 1 to 10

The factorial of a number 'N' represents the product of integers from 1 to N. Learn the steps to calculate factorial values from 1 to 10 and its use in statistics. ... In this article we will learn all about what is factorial in mathematics? Factorial definition is very simple - Factorial is ...

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Factorial Calculator

The factorial calculator computes factorials of non-negative integers, representing the fundamental mathematical operation n! = n × (n-1) × (n-2) × ... × 2 × 1, with 0! = 1 by definition. Factorials appear throughout mathematics, particularly in combinatorics where they count permutations ...

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How many zeros are there in 10 factorial? - Quora

So the factors of 10 which results product 10 and present in 1–10 are 1×10 and 2×5. Product of no other numbers present between 1 to 10 except these will result into 10 or have ...

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How to Calculate a Factorial (Plus Examples and FAQ) | Indeed.com Canada

In the example above, five is the starting number. You can also use larger numbers to calculate a factorial. For example, the factorial of 10 is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, which equals 3,628,800.

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Factorial Calculator Online - Find Factorial Easily

The factorial of a number is the product of all positive integers less than or equal to that number. It is represented by an exclamation mark (!) placed after the number. For example, the factorial of 5 (written as 5!) is calculated as 5 × 4 × 3 × 2 × 1, which equals 120.

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Factorial Notation

*Factorial notation* allows you to write multiplication patterns like 10x9x8x7x6x5x4x3x2x1 very efficiently---it goes by the name 10! (read aloud as 'ten factorial'). This notation is efficient, compact, and is particularly useful in formulas for combinations and permutations.