Multiply every positive integer through n and return the exact whole-number result. Its factorial sits beside the working formula for a quick arithmetic check.
The factorial n! is the product n(n−1)…2·1, with 0!=1 by the empty-product convention. Its rapid growth records how many orders are possible for n distinct objects. Factorial can also be compared with double factorial.
On this page, the displayed factorial follows this definition rather than any similarly named measure.
Start from one and multiply by each successive integer through n. Preserve the integer result rather than converting it to a floating-point approximation.
For n=10, multiply 1 through 10 to obtain 3,628,800. The ratio 10!/9!=10 provides a short independent check. This Factorial example can be compared with combination counts.
Factorials appear in permutations, combinations, probability distributions, Taylor series, and recursive counting arguments. Exact integer output matters because rounded scientific notation can hide divisibility.
Factorial applies to nonnegative integers in this page. It should not be confused with repeated multiplication n^n, and very large answers may contain thousands of digits.
Keep any applicable units beside the source values; the browser cannot detect a silent mismatch during factorial.
Treat each labeled field as part of the definition, not merely an empty box. The field assignment determines what the displayed factorial describes. Convert measured values to compatible units first and retain their original precision until the final rounding choice.
Moving from n to n+1 multiplies the answer by exactly n+1, so even a one-step input change can be dramatic. Predict that movement before recalculating the factorial; disagreement points to an input-role or sign issue.
Report the factorial at a precision justified by the inputs. A long browser decimal is computational detail, not evidence that the source values were measured that accurately. When an exact symbolic form is conventional, keep it beside the rounded value so later work is not forced to reuse an early approximation.
Double factorial skips every other integer; ordinary factorial includes every positive integer up to n. Here the requested quantity is specifically factorial.
Keep the supplied input with the result, including any units and the final rounding place. The displayed formula then preserves how the factorial was obtained.
Keep the Nonnegative integer n labels beside the answer and reconstruct one small case by listing its outcomes. For Factorial, agreement between a direct list and the formula checks the interpretation as well as the arithmetic. Preserve exact integers and unrounded probabilities until the comparison is complete.
For Factorial, then change one input whose effect is predictable. If the result moves in the opposite direction, review whether order, replacement, overlap, or conditioning was assigned correctly before adjusting the displayed precision.
It preserves counting identities and represents one empty arrangement.
No.
Not in this elementary integer definition.
Their ratio should equal the larger index.