What is the value of 100 factorial (100!)?

The value of 100 factorial (100!) is the product of all natural numbers from 1 to 100.

Definition:

• 100! = 100 × 99 × 98 × ... × 3 × 2 × 1

Exact Value:
100! =
933262154439441526816992388562667004907159682643816214685929
638952175999932299156089414639761565182862536979208272237582
51185210916864000000000000000000

Key Insight:

• Factorials grow extremely fast, so values become very large even for moderate numbers like 100.
• Because of this, calculators and computers are usually used to compute such values.

Scientific Notation (Approximate):

• 100! = 9.33 × 10¹⁵⁷

Applications:

• Used in permutations and combinations
• Important in probability and statistics
• Used in advanced mathematics and computer science

Exam Tip:

• You are usually not required to write the full value.
• Focus on understanding the concept and representation.