What is 52 factorial ?

Steps to calculate factorial of 52

To find 52 factorial, or 52!, simply use the formula that multiplies the number 52 by all positive whole numbers less than it.

Let’s look at how to calculate the Factorial of 52:

52! is exactly :
8.05 x 10^67
Factorial of 52 can be calculated as:
52! = 52 x 51 x 50 x 49 x … x 3 x 2 x 1

Factorials of Numbers similar to 52

What is Factorial?

Factorial, indicated by the symbol ‘!’, represents the product of all positive integers up to a given number. The factorial of 52, denoted as 52!, is especially significant in mathematics due to the vast number of permutations it can express, given its relation to combinatorial problems and probability calculations.

Formula to Calculate the Factorial of 52

The calculation for 52 factorial follows the formula n! = n × (n-1) × … × 1. For the number 52, it entails multiplying every natural number from 52 down to 1. As a concrete example, the initial steps would look like 52 × 51 × 50 × … × 3 × 2 × 1.

What is the Factorial of 52 Used For?

The factorial of 52 can be particularly notable in areas like combinatorics, where it can represent the number of ways to order a deck of cards. It also surfaces in probability theory and can be seen in algorithms that rely on understanding the total possible permutations of a set.


  • How many distinct arrangements can be made using all cards in a standard deck?
  • If you were to take one card out of a deck, how many arrangements would be possible with the remaining cards?

Solutions to Exercises

  1. Since a standard deck contains 52 cards, the number of different arrangements is equal to 52!, which is a substantial number beyond the scope of manual calculation.
  2. With one card removed, 51 cards remain, thus the number of distinct arrangements is 51!.

Frequently Asked Questions

Q: What is the numerical value of 52 factorial?

A: The value of 52 factorial is extraordinarily large, and it is generally expressed in scientific notation as approximately 8.0658e+67.

Q: What is the significance of the factorial function in mathematics?

A: Factorials are foundational in combinatorics, probability, and algebra. They represent the number of ways to arrange a set of unique items and are critical to calculating permutations and combinations.

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