What is 64 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.

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.

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.

• 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?

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.