Math Problem Statement

Simplify 8!

Solution

The factorial of 8, denoted as 8!8!, is the product of all positive integers from 1 to 8:

8!=8×7×6×5×4×3×2×1=40,3208! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40,320

So, 8!=40,3208! = 40,320.

Would you like further details on factorials or any other questions?

Here are 5 related questions to explore:

  1. What is the value of 10!10!?
  2. How can factorials be used in permutations and combinations?
  3. What is the factorial of zero, 0!0!, and why?
  4. How would you simplify 8!÷6!8! \div 6!?
  5. Can you express factorials in terms of recursive functions?

Tip: Factorials grow very quickly! Even relatively small numbers like 20 have huge factorials.

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Math Problem Analysis

Mathematical Concepts

Factorial
Number Theory

Formulas

n! = n × (n-1) × (n-2) × ... × 1

Theorems

Factorial Growth Theorem

Suitable Grade Level

Grades 8-10