What is the Factorial of 100?: In mathematics, factorial means multiplying a number by every whole number smaller than it, down to 1. It is written using an exclamation mark (!) and is used in many math topics like counting, probability, and arrangements.
As the number increases, its factorial value also increases. That’s why when we look at the factorial of 1 to 100, we see that each answer is much greater than the previous one. This often makes students curious to ask, "What is the factorial of 100?" and how big can it be?
To find this out, we simply multiply 100 × 99 × 98 and continue till 1. This is called the factorial of hundred, and the answer is a number with 158 digits. Keep reading to learn what is the factorial of hundred and why it is an important concept in math.
Read More: Factorial
What is Factorial?
Before we learn about the factorial of 100, it’s important to understand what the word factorial means in math. A factorial is when we multiply a number by all the whole numbers smaller than it, down to 1.
For example, if we take any number “n,” then its factorial is written as n! (read as “n factorial”). It means: n! = n × (n – 1) × (n – 2) × … × 3 × 2 × 1. So, factorial is just the product of all numbers from 1 to that number.
What is the Factorial of 100?
Now that we understand what factorial means, let’s understand what is the factorial of 100, also called 100 factorial or written as 100! It means multiplying all the whole numbers from 100 down to 1. So, the full expression looks like this: 100 × 99 × 98 × ... × 3 × 2 × 1.
Because 100 is a large number, doing all these multiplications gives us a result that is really big. This is why mathematicians use a short form called scientific notation to write the answer easily. The factorial of 100 is written as: 100! = 9.332621544 × 10¹⁵⁷
This means the number has 158 digits, which is too big to write normally. As the numbers increase, the factorial becomes much larger with each step. Now here are some amazing facts about the factorial of hundred:
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It has exactly 158 digits.
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It ends with 24 zeros, which we call trailing zeros.
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The exact factorial of hundred is:
93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000
Read More: Equation
What is the Negative Factorial of Hundred?
While learning about factorials, one common question that comes up is, "What is the factorial of 100 if the number is negative? Can we find the factorial of –100?" The answer is no. In mathematics, factorial is not defined for negative numbers. This means we cannot find the factorial of –100 or any other negative number.
Let’s understand why. Factorial means multiplying a number by all whole numbers less than it, down to 1. But negative numbers don’t follow that pattern. If we try to use the factorial rule backward, we get stuck at 0! (zero factorial), which is 1.
So, the factorial of hundred is a very large number, but the factorial of –100 is not possible in math. That’s why we only find factorials for non-negative whole numbers (like 0, 1, 2, 3… and so on).
Read More: Dimensional Formula
Properties of Factorial
Factorials follow some special rules and patterns in mathematics. These rules help us understand how factorials work and how we can use them in different math problems.
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For any number n, the factorial of n means multiplying it by every number smaller than it till 1. So, n! = n × (n - 1) × (n - 2) × ... × 2 × 1.
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A special rule is: n! = n × (n - 1)! This means we can also find a factorial by multiplying the number with the factorial of the number before it.
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0! is always 1. This is a fixed rule in math, even though 0 has no numbers below it to multiply.
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Factorials are always whole numbers (integers). You will never get a decimal or fraction as the result of a factorial.
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We can also use a math symbol called a product sign (∏) to write factorials:
n! = ∏(i = 1 to n) i — This means multiply all numbers from 1 to n.
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Negative numbers don’t have factorials. That means factorial is only defined for 0 and positive whole numbers.
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Factorials increase very quickly. For example, 10! = 3,628,800 and 15! = 1,307,674,368,000. The bigger the number, the faster the factorial increases.
Also Read: Rational Numbers
Uses of Factorial in Maths
Factorials are not just number patterns; they are used in many areas of math that help us solve real problems. Let’s look at where and how factorials are useful.
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Counting and Arrangements (Combinatorics): Factorials are used when we want to count how many ways we can arrange or choose things. For example, if students want to find out how many ways they can sit in a row, factorials help to find that number. This is used in topics like permutations and combinations.
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Probability: In probability, we try to find out how likely something is to happen. Factorials are used to calculate the number of possible outcomes in games or experiments. For example, in card games or coin tosses, we use combinations and factorials to find chances.
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Statistics: In statistics, factorials are used in formulas that help us study data and numbers. Some important topics where factorials are used include binomial coefficients and Poisson distribution, which help in analyzing results and making predictions.
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Mathematical Series: Factorials are also used in special types of math formulas like Taylor series and Maclaurin series. These are used to write big and complex functions in a simpler form using a sum of many terms. Factorials appear in these formulas to make the math work correctly.
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Games and Puzzles: Factorials help us find how many ways we can arrange things in games. Whether it’s arranging cards or solving number puzzles, factorials tell us how many different ways it can be done.
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Computer Programming: In coding, factorials are used in programs that need to solve math problems. Programmers use them to create logic for finding all arrangements or combinations of items quickly.
So, factorials are more than just multiplying numbers; they help us in counting, solving puzzles, understanding chances, and even in writing computer programs.
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