Trailing zeros in 40 factorial = 9
Quick Answer:
9 trailing zeros in 40!
Legendre's Formula: Count factors of 5 in 40!
⌊40/5⌋ = 8 + ⌊40/25⌋ = 1 = 9
Factorial Calculator Until 10,000
Nearby Factorials
| n | n! | Digits | Trailing Zeros |
|---|---|---|---|
| 35! | 10333147...0000 | 41 | 8 |
| 36! | 37199332...0000 | 42 | 8 |
| 37! | 13763753...0000 | 44 | 8 |
| 38! | 52302261...0000 | 45 | 8 |
| 39! | 20397882...0000 | 47 | 8 |
| 40! | 81591528...0000 | 48 | 9 |
| 41! | 33452526...0000 | 50 | 9 |
| 42! | 14050061...0000 | 52 | 9 |
| 43! | 60415263...0000 | 53 | 9 |
| 44! | 26582715...0000 | 55 | 9 |
| 45! | 11962222...0000 | 57 | 10 |
Here you can find answers to questions like: What is the number of zeros on the end of 40 factorial What is the factorial of 40? What is the last digits of factorial of 40? How many trailing zeros in 40 factorial? How many digits are there in 40 factorial? Use the factorial calculator above to find the factorial of any natural between 0 and 10,000.
What is factorial?
Definition of factorial
The factorial is a quantity defined for any integer n greater than or equal to 0.
The factorial is the product of all integers less than or equal to n but greater than or equal to 1. The factorial value of 0 is, by definition, equal to 1. For negative integers, factorials are not defined. The factorial can be seen as the result of multiplying a sequence of descending natural numbers (such as 3 × 2 × 1).
The factorial symbol is the exclamation mark (!).
The factorial formula
If n is a natural number greater than or equal to 1, then
n! = n x (n - 1) x (n - 2) x (n - 3) ... 3 x 2 x 1
If n = 0, then n! = 1, by convention.
Example: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Shortcut to find trailing zeros in a factorial
Trailing zeros are a sequence of zeros in the decimal representation of a number, after which no other digits follow. This video shows how to find the trailing zeros of a factorial easily.
Table of factorials until 30
| n | n! | |
|---|---|---|
| 1! | 1 | # |
| 2! | 2 | # |
| 3! | 6 | # |
| 4! | 24 | # |
| 5! | 120 | # |
| 6! | 720 | # |
| 7! | 5040 | # |
| 8! | 40320 | # |
| 9! | 362880 | # |
| 10! | 3628800 | # |
| 11! | 39916800 | # |
| 12! | 479001600 | # |
| 13! | 6227020800 | # |
| 14! | 87178291200 | # |
| 15! | 1307674368000 | # |
| 16! | 20922789888000 | # |
| 17! | 355687428096000 | # |
| 18! | 6402373705728000 | # |
| 19! | 121645100408832000 | # |
| 20! | 2432902008176640000 | # |
| 21! | 51090942171709440000 | # |
| 22! | 1124000727777607680000 | # |
| 23! | 25852016738884976640000 | # |
| 24! | 620448401733239439360000 | # |
| 25! | 15511210043330985984000000 | # |
| 26! | 403291461126605635584000000 | # |
| 27! | 10888869450418352160768000000 | # |
| 28! | 304888344611713860501504000000 | # |
| 29! | 8841761993739701954543616000000 | # |
| 30! | 265252859812191058636308480000000 | # |
Frequently Asked Questions
How many trailing zeros are in 40 factorial?
There are 9 trailing zeros in 40!. This is calculated using Legendre's formula: count how many times 5 divides into 40, then 25, then 125, and so on, adding up all the quotients.
What is Legendre's formula?
Legendre's formula calculates the number of trailing zeros in n! by summing ⌊n/5⌋ + ⌊n/25⌋ + ⌊n/125⌋ + ... until the quotient becomes 0. Each trailing zero comes from a factor of 10, which requires one factor of 2 and one factor of 5.
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