FACTDOUBLE in Apple Numbers: Double Factorials with Examples

FACTDOUBLE multiplies every second positive integer counting down from the specified number. The double factorial 7!! means 7×5×3×1 = 105, not (7!)! and not FACT(7). For even values, 8!! = 8×6×4×2 = 384. The expected result for =FACTDOUBLE(7) is 105. [A1, M1]

Official syntax and arguments

=FACTDOUBLE(fact-num)

Apple’s spelling and argument name are exactly FACTDOUBLE(fact-num). The one required argument is a numeric value or numeric cell reference. Apple’s accepted fact-num must be greater than or equal to −1. Values in [−1, 1] give 1; any fractional portion is discarded. There are no optional arguments or documented defaults. FACTDOUBLE(-2) violates the documented domain; do not infer a precise native-app error string. [A1]

The English function name above appears in Apple’s Formulas and Functions Help 15.4, consulted on 2026-10-12T02:47:22Z UTC. The help-edition number identifies the documentation that was checked; it does not establish the minimum Numbers application version, the introduction date, identical availability on macOS, iOS, iPadOS and iCloud.com, or a translated function-name alias. Those details require platform-specific verification before a compatibility claim is published. No official English alternative function name was found in the checked catalogue. [A1, A2]

Apple’s standard function examples separate arguments with commas. If your system’s decimal separator is a comma, Apple instructs you to use semicolons between arguments entered manually. In that setting, a formula written here as =GCD(24,36) may need =GCD(24;36); the appropriate decimal notation for 24.5 will also differ. Enter the function from Numbers’ Functions Browser to avoid locale-related typing mistakes. [A3]

A same-table formula can refer to B2; a range is B2:B6. When a function is entered in a different table, select the source cells with the editor so Numbers inserts a qualified reference such as SourceTable::B2 or Sheet 2::SourceTable::B2. The exact sheet/table names depend on the workbook. Apple documents :: as the cross-table/sheet qualifier; Excel Sheet1!A1 syntax is not the same. [A4]

Validation status: Official Apple documentation checked; example outcomes independently reasoned and calculated in Python, except where clearly labelled an Apple-documented error. Not executed in Apple Numbers. Numerical outcomes below are expected, not observed app results. No genuine Numbers screenshots were available; this guide contains no mock application images.

Create one Numbers table named DoubleFactorials. Put Input in B1 and Expected result in C1. Enter the following as numeric values in column B, starting in B2; in C2 type =FACTDOUBLE(B2), then fill down. The C-column values are independent mathematical expectations, not Apple Numbers observations. [A1, M1]

Row: 2

B — Input
−1

C — Formula
=FACTDOUBLE(B2)

C — expected
1

Row: 3

B — Input
0

C — Formula
=FACTDOUBLE(B3)

C — expected
1

Row: 4

B — Input
1

C — Formula
=FACTDOUBLE(B4)

C — expected
1

Row: 5

B — Input
2

C — Formula
=FACTDOUBLE(B5)

C — expected
2

Row: 6

B — Input
3

C — Formula
=FACTDOUBLE(B6)

C — expected
3

Row: 7

B — Input
4

C — Formula
=FACTDOUBLE(B7)

C — expected
8

Row: 8

B — Input
5

C — Formula
=FACTDOUBLE(B8)

C — expected
15

Row: 9

B — Input
6

C — Formula
=FACTDOUBLE(B9)

C — expected
48

Row: 10

B — Input
7

C — Formula
=FACTDOUBLE(B10)

C — expected
105

Row: 11

B — Input
8

C — Formula
=FACTDOUBLE(B11)

C — expected
384

Row: 12

B — Input
10

C — Formula
=FACTDOUBLE(B12)

C — expected
3,840

Row: 13

B — Input
4.7

C — Formula
=FACTDOUBLE(B13)

C — expected
8

Check by hand: FACTDOUBLE(6) = 6×4×2 = 48; FACTDOUBLE(5) = 5×3×1 = 15. 4.7 is treated as 4 by the documented discard-fraction rule. When entering negative one, use the actual numeric -1, not a pasted Unicode minus character. A locale using decimal comma may display or accept 4,7 instead of 4.7. [A1, A3, M1]

For a positive even integer 2n, the product is (2n)!! = 2×4×...×(2n). For a positive odd integer 2n−1, the product is (2n−1)!! = 1×3×...×(2n−1). Apple explicitly documents separate even/odd product definitions. As mathematical identities rather than newly tested Numbers behaviours, (2n)!! = 2^n n! and (2n−1)!! can count ways to split 2n labelled objects into unordered pairs. [A1, M1]

Count unordered pairs of people

Six distinct people can be arranged into three unordered pairs in 5×3×1 = 15 ways. Enter =FACTDOUBLE(5) to obtain the expected 15. In a table Pairings, put the number of pairs, 3, in B2, then use =FACTDOUBLE(2*B2-1) in C2; expected 15. For four pairs (eight people), the same expression gives 7!! = 105. The interpretation assumes every participant appears in exactly one pair and pair order does not matter. [M1]

Check the even-number identity using FACT

In a new calculation cell, enter =FACTDOUBLE(8): expected 384. Compare with =POWER(2,4)*FACT(4): expected 384 because 16×24=384. Both POWER and FACT are separately documented Apple functions. This is a useful independent arithmetic check, not a claim that the composed formula was run inside Numbers. [A1, M1]

Detect noninteger data before applying FACTDOUBLE

If B2 is supposed to count whole items, a numeric value 4.7 silently maps to 4!! = 8. To flag potentially accidental decimals, place =B2=TRUNC(B2) in a separate validation column for a verified numeric input; this compares the value to the integer part. It checks whole-valuedness, not the ≥−1 domain. Add a separate rule =B2>=-1 if your workflow requires explicit domain checking. Apple documents TRUNC as its own function. [A1, M1]

Cross-table input

If the input B2 resides in DoubleFactorials but the result is elsewhere, select B2 from the other table using the Formula Editor. It may insert =FACTDOUBLE(DoubleFactorials::B2); do not assume that text is accepted if the actual table name differs. In a different sheet, the editor can qualify both the sheet and table. [A4]

An input cell containing a string that looks numeric, a date/duration, an empty cell, or a Boolean was not tested. No implicit coercion or exact error code is asserted. Do not rely on an unverified maximum argument size or an unverified result-precision threshold.

Microsoft Excel and Google Sheets list a same-named FACTDOUBLE function with the same mathematical purpose. For the positive-integer examples above, the expected mathematics is portable. This does not establish identical handling of empty cells, textual numbers, noninteger negatives, error text, precision or locales. If importing a workbook, recompute the test table in the target program rather than assuming complete behavioral equivalence. [X1, X2]

Apple FACT explains ordinary factorials; Apple MULTINOMIAL is another combinatorial function, linked from the FACTDOUBLE reference. These are official links, not claims that any related page exists at a new URL on Spreadsheet-Tutorials.com. [A1]

• [A1] Apple, FACTDOUBLE, Formulas and Functions Help 15.4 (accessed 2026-10-12T02:47:22Z). Official function article. Claim support: syntax, argument requirements, documented examples and domain/behaviour notes; see the article’s main-content 420–434 main-content lines in the collected research evidence.
• [A2] Apple, List of functions by category, checked 2026-10-12T02:47:22Z. Confirms the English canonical function name and its Numeric grouping, but is not a minimum-version compatibility matrix.
• [A3] Apple, Functions overview, checked 2026-10-12T02:47:22Z. Confirms required vs optional argument notation, case-insensitive function spelling and comma/semicolon conventions.
• [A4] Apple, Refer to cells in formulas and Types of arguments and values, checked 2026-10-12T02:47:22Z. Explains ranges, qualified table references, numeric values and collections.
• [X1] Microsoft, Excel math and trigonometry reference, checked 2026-10-12T02:47:22Z. Confirms the presence of the same named function; engine-specific coercion and corner cases are not assumed identical.
• [X2] Google, Google Sheets function list, checked 2026-10-12T02:47:22Z. Confirms name/purpose; Sheets syntax and locales should be checked in a Sheets workbook.
• [M1] Independent Python standard-library computation performed for the explicit numeric test vectors recorded in the accompanying JSON evidence; no Apple Numbers application execution.

• FACT — continue with a related Apple Numbers calculation.
• COMBIN — continue with a related Apple Numbers calculation.
• COMBINA — continue with a related Apple Numbers calculation.
• PERMUT — continue with a related Apple Numbers calculation.
• PERMUTATIONA — continue with a related Apple Numbers calculation.

For a software-specific comparison: LibreOffice Calc FACTDOUBLE, Apache OpenOffice Calc FACTDOUBLE, Gnumeric FACTDOUBLE. A shared name does not establish identical argument, error or version behaviour.

The linked official function documentation was reviewed on October 12, 2026. Apple’s Formulas and Functions Help 15.4 identifies the documentation edition, not a minimum Numbers release or a guarantee of historical platform parity. Selected worked examples were checked using independent mathematical or text-processing models; results are expected values, not observations from the spreadsheet application. Native Apple Numbers execution was not performed. Undocumented coercion, exact error messages and platform-specific behaviour remain unverified.

View reproducible example inputs and independent check results. This record is not a native spreadsheet test log.