Multifactorial Calculator
Expand beyond the standard factorial. This tool calculates products that skip numbers, like the double factorial (n!!) or any custom step-factorial.
Formula:
n(!...!) [k times] = n × (n-k) × (n-2k) × ...
(Product stops at the last positive integer)
5!! (Double factorial): 5 × 3 × 1 = 15 6!!: 6 × 4 × 2 = 48 7!!! (Triple factorial): 7 × 4 × 1 = 28
What is a double factorial (n!!)?
The double factorial of a number n is the product of all integers from n down to 1 that have the same parity (even or odd) as n. For example, 5!! = 5 × 3 × 1 = 15, and 6!! = 6 × 4 × 2 = 48.
How do multifactorials work?
A k-factorial (denoted by k exclamation marks) skips k-1 numbers in the product. For example, a triple factorial n!!! multiplies every third number: n × (n-3) × (n-6) ...
Is n!! the same as (n!)!?
No! The double factorial n!! is NOT the same as the factorial of a factorial. For example, (3!)! = 6! = 720, while 3!! = 3 × 1 = 3.
What is 0!!?
By definition, 0!! = 1. This is consistent with the empty product convention in mathematics.
🔗 Related Calculators
📐 Formula
Formula:
n(!...!) [k times] = n × (n-k) × (n-2k) × ...
(Product stops at the last positive integer)
📝 Example Calculation
5!! (Double factorial): 5 × 3 × 1 = 15 6!!: 6 × 4 × 2 = 48 7!!! (Triple factorial): 7 × 4 × 1 = 28
❓ Frequently Asked Questions
What is a double factorial (n!!)?▼
The double factorial of a number n is the product of all integers from n down to 1 that have the same parity (even or odd) as n. For example, 5!! = 5 × 3 × 1 = 15, and 6!! = 6 × 4 × 2 = 48.
How do multifactorials work?▼
A k-factorial (denoted by k exclamation marks) skips k-1 numbers in the product. For example, a triple factorial n!!! multiplies every third number: n × (n-3) × (n-6) ...
Is n!! the same as (n!)!?▼
No! The double factorial n!! is NOT the same as the factorial of a factorial. For example, (3!)! = 6! = 720, while 3!! = 3 × 1 = 3.
What is 0!!?▼
By definition, 0!! = 1. This is consistent with the empty product convention in mathematics.