How to calculate factorial easily?

In mathematics, the factorial of a number is found by the multiplication of the number with every positive integer less than that. So, n!= n × (n-1) × (n-2) × (n-3) × ..... × 3 × 2 × 1 .

Is there a faster way to calculate Factorials?

You can compute a factorial quickly using a scientific calculator , which should have a. {\displaystyle x!} sign. If you are computing by hand, to make it easier, first look for pairs of factors that multiply to equal 10.

How do you answer a factorial question?

You can follow these steps to solve for a factorial: Determine the number. Determine the number you are finding the factorial of. ... Write the sequence. Using the factorial formula, you can write out the sequence of numbers that you'll multiply. ... Multiply the numbers. Oct 22, 2023

What is the answer to the 5 factorial?

To find 5 factorial, or 5!, simply use the formula; that is, multiply all the integers together from 5 down to 1 . When we use the formula to find 5!, we get 120. So, 5! = 120.

What is the shortcut for calculating factorials?

There is no shortcut to find a factorial of a number . In maths, generally only upto 7! is used in calculation. You can learn till 7! only after that it is not recommended.

What is the factorial formula simplified?

The factorial operation, n!, is defined as n! = n(n – 1)(n – 2)(n – 3) · · · 4 · 3 · 2 · 1 . In other words, you multiply the number n, being operated upon, by every positive integer smaller than n.

What is the general formula for a factorial?

In short, a factorial is a function that multiplies a number by every number below it till 1. For example, the factorial of 3 represents the multiplication of numbers 3, 2, 1, i.e. 3! = 3 × 2 × 1 and is equal to 6.

What are factorials for dummies?

To find a number's factorial, you write all the whole numbers from 1 to that number and then multiply them all together . For example, 5! (read as "five factorial") is shorthand for 1 × 2 × 3 × 4 × 5, which you can work out on your calculator to get the value 120.

Answer: yes. actually 4! = 4×3×2×1 = 24 ......

How to calculate a factor?

Thus, to find all the factors of a number, find all the pairs of numbers that, when multiplied, give the given number as a product . As a result, the factors of 8 are 1, 2, 4, 8. The factors of 18 are 1, 2, 3, 6, 9, and 18. We can find the factors of a number by dividing the number by all possible divisors.

How do you solve a factorial in probability?

A factorial is written as the number followed by an exclamation point. For example, to write the factorial of 4, you would write 4!. To calculate the factorial of 4, you would multiply all of the positive integers equal to and less than 4 . So, 4!

What is the simple equation for factorial?

Factorial is the operation of multiplying any natural number with all the natural numbers that are smaller than it, giving us the mathematical definition n! = n * (n - 1) * (n - 2) * (n - 3) .... Lastly, factorial is used for questions that ask you to find how many ways you can arrange or order a set number of things.

What is factorial formula?

A factorial is a mathematical operation that you write like this: n! . It represents the multiplication of all numbers between 1 and n. So if you were to have 3! , for example, you'd compute 3 x 2 x 1 (which = 6).

How to calculate 20 factorial?

Solution: A factorial of a number is the function that multiplies the number by every natural number below it . The Factorial of n is denoted by n! Thus, the factorial of 20 is 2432902008176640000.

Calculate each Factorial: | Wyzant Ask An Expert (2024)

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Ally J.

asked 05/03/21

a) 30x4! The answer is 720 when you plug it in the calculator, but how can make it to be 6!, 6! = 720, if that makes sense.

b) 7 / 2! 5! + 7! / 4! 3!

I did, 7x6x4x3 = 504, 7x6x5 / 3x2x1 = 84, 84 + 504 = 588 but the answer was supposed to be 56.

c) 9! / 3! 6!

I did 9x8x7x5x4 = 10,080 but the answer was 84.

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Vidya V.

tutor

Part a) 30*4! = 6*5*4!= 6!Part c) If you do:(9x8x7x6x5x4x3x2x1)/(3x2x1)(6x5x4x3x2x1)=(9x8x7)/(3x2x1)You’ll get the answerI think you might have missed some number Part b) would be 21+ 35= 56I see your mistake now!Ok what you’re doing is you’re just removing the denominator numbers from the numerator- but in the denominator you have 2!*5! Which means your denominator would be (2x1)(5x4x3x2x1)Now you cancel out some numbers in the numbers for and denominator and you would end up having 21 and 35.I hope I have helped you understand.

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05/03/21

Ally J.

Thank you!!

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05/03/21

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James C. answered 05/03/21

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The key here is to remember what factorials look like when "expanded" out. In general,

n! = n x (n-1) x (n-2) x , , , x 2 x 1

7! = 7x6x5x4x3x2x1

So, for part a, we can make the expression look like 6! by doing the following

30x4! = 30x4x3x2x1

Notice that 30 = 6x5

30x4x3x2x1 = 6x5x4x3x2x1 = 6!

For part b, if we expand out each factorial, we will see a lot of cancelling between the numerator and denominator. I will give an example of the second half of part b and then let you take it from there.

7! / 4! 3! = 7x6x5x4x3x2x1 / (4x3x2x1)x(3x2x1)

Notice that 3x2x1 = 6

7x6x5x4x3x2x1 / (4x3x2x1)x6

Now notice that there is a 4,3,2,1, and 6 on top and bottom of the fraction, so we can cancel those out,

7x5 = 35

(remember that this is only the second half of part b, you can confirm that the first half is equal to 21, meaning the answer is 56 as you said)

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Ally J.

Thank you so much, but what if it was a bigger number like 90x8! Or 20x19! ? Second part, But the thing that I’m confused about is that it is very similar to question that I did before which is 9! / 3! 6!, 9x8x7x6x5x4x3 (up to 3!) cancel the 3! numerator and denominator and the 6! as well, and my answer was 10,080 which was correct. Did the exact same thing, that’s why I was confused.

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05/03/21

James C.

tutor

For the first part, this process will work regardless of the size of the number. They key is to factor the larger number into numbers that can be "absorbed" into the factorial, for the example you gave, 90x8! = 10x9x8! = 10!As for the second part, it is hard to give a definite answer without seeing the problem you are talking about. It is also possible to just get lucky and make 2 mistakes that cancel each other out when calculating a factorial like these. This method will definitely get you the correct result every time, though.

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05/03/21

Ally J.

For 20x19! I did (5x4=20) 5x4x3x2x1 = 5! Which was incorrect. I realised my mistake for part b) your way was better!

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05/03/21

Ally J.

Also what if it was 21! / 17!4!, I did 21x20x19x18x17x16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1 / (17x16x15x14x13x12x11x10x9x8x7x6x5x3x2x1)x(4x3x2x1)=24, so cancel 17s,16s,15s,14s.....1s I was left with 21x20x17x18 / 4x3x2x1, and still got the answer wrong.

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05/03/21

Raymond B. answered 05/03/21

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a) 30 x 4! = 6 x 5 x 4! = 6! (30=6x5)

6! = 30 x 4! = 720

either = 6(5)(4)(3)(2)(1) = 30x24= 720

b) 7!/2!5! + 7!/3!4! = 7(6)/2 + 7(6)(5)/3(2) = 21 +35 =56

You seem to have omitted ! after the first 7

c) 9!/3!6! = 9(8)(7)/3(2) = 3(4)7) = 84

9!= 9(8)(7)(6!) the 6! cancels with the 6! in the denominator leaving

9(8)(7)/3(2)(1). 3 divides into 9 = 3 and 2 divides into 8 = 4 leaving

3(4)(7) = 12(7) = 84

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