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# What is 64 factorial ?

Steps to calculate factorial of 64

To find 64 factorial, or 64!, simply use the formula that multiplies the number 64 by all positive whole numbers less than it.

Let’s look at how to calculate the Factorial of 64:

64! is exactly :
1.27 x 10^89
Factorial of 64 can be calculated as:
64! = 64 x 63 x 62 x 61 x … x 3 x 2 x 1

## What is Factorial?

A factorial, denoted by an exclamation mark (!), is a function that multiplies a number by every positive integer below it down to one. The factorial of 64, or 64!, is of special interest in mathematics due to its use in combinatorial problems, large-scale calculations, and other advanced mathematical applications. Understanding 64 factorial is fundamental for grasping its extensive implications and applications.

## Formula to Calculate the Factorial of 64

The basic formula to calculate a factorial is n! = n × (n-1) × … × 1. To calculate 64 factorial, one would compute:

64! = 64 × 63 × 62 × … × 3 × 2 × 1.

Due to the enormity of this number, it is typically computed with computer software when exact values are needed.

## What is the Factorial of 64 Used For?

The factorial function, particularly 64 factorial, has important applications in several fields. For example:

• Combinatorics: Determining the number of combinations and permutations in a set of 64 items.
• Probability Theory: Calculating probabilities in complex scenarios involving 64 different outcomes or elements.
• Computer Science: Designing algorithms that deal with arrangements or sequences involving 64 characters or elements.

## Exercises

• How many zeros are at the end of the value of 64!?
• If you have 64 different books, in how many ways can you arrange them on a shelf?

## Solutions to Exercises

1. The number of trailing zeros in 64! is determined by the number of times the number 10, which is 2 × 5, can be factored into the product. Since there are more factors of 2 than 5, we count the occurrences of 5, which is 14.
2. The number of ways you can arrange 64 books on a shelf is directly given by 64!, which signifies the total permutations of 64 unique items.