FACT Function in Apple Numbers: Factorials, Arguments and Real Examples

FACT calculates a nonnegative integer factorial. In Apple Numbers, =FACT(5) has an expected result of 120 because 5! = 5×4×3×2×1. =FACT(0) has an expected result of 1; a noninteger argument has its fractional part discarded before the factorial is calculated ([A1]).

Official syntax (Apple Formulas and Functions Help 15.4):

=FACT(fact-num)

Required input: fact-num is a single numeric expression, literal, or numeric cell reference. Apple documents one required argument, no optional arguments, and no defaults for this function. The argument’s type matters: a visually number-like text cell is not equivalent to a verified numeric input. Syntax, argument names, and documented behavior are sourced from the official Apple FACT reference ([A1]).

Function name, release, references, and locale

• Name/aliases: FACT is the English name present in Apple’s checked function catalogue; no distinct official alias was established in that English entry. Do not create separate pages for localized labels or version variants without evidence ([A2]).
• Documentation scope: The reference is the public Apple Formulas and Functions Help edition 15.4, accessed on 2026-10-12 UTC. A help-edition number is not the minimum supported Numbers application version. We did not establish introduction dates, identical platform support, or localized aliases across Mac/iPhone/iPad/web ([A1], [A2]).
• Decimal conventions: English formula examples use . as the decimal point. Apple documents using semicolons between arguments when a decimal comma is configured. This function has only one argument, so there is no separator inside =FACT(fact-num); the decimal literal 2.5 may need localized entry as 2,5. Insert cells using the formula editor to avoid mistaken punctuation ([A3]).
• Cell references: In the same table, B2 is a relative reference; when a formula references another table, Numbers uses a qualified token such as DataTable::B2. A reference on another sheet can include its sheet and table names, and selection from the editor is safer than manually constructing a name with spaces. Verify the actual table/sheet names before copying a cross-table formula ([A4]).

Official supporting guidance: Function syntax, capitalization and regional separators; Refer to cells in formulas.

Domain and numeric-argument rules

The official Apple reference requires a numeric fact-num at least zero. For nonintegers, Numbers discards the fractional part before evaluation, so =FACT(4.5) has the documented expected result of 24 (4!). A negative input such as =FACT(-1) is a documented error condition; we have not established an exact native error string or observed an app error cell ([A1]). Factorials grow very rapidly; this tutorial does not claim a tested largest accepted integer, overflow threshold, or internal numeric precision for Apple Numbers.

Create a table named FactorialPractice with A = Item, B = Input (number), and C = Factorial result. Enter the exact numeric B-column inputs below beginning in row 2. In C2 type =FACT(B2) and fill down. Values in the output column were computed with Python math.factorial(int(value)) for nonnegative values (truncation toward zero for positive decimals) and cross-checked with Apple’s example for 0, 4.5, and 5. They are expected results, not app observations ([A1], [M1]).

Row: 2

B: numeric input
0

C: formula
=FACT(B2)

C: expected result
1

Row: 3

B: numeric input
1

C: formula
=FACT(B3)

C: expected result
1

Row: 4

B: numeric input
2

C: formula
=FACT(B4)

C: expected result
2

Row: 5

B: numeric input
3

C: formula
=FACT(B5)

C: expected result
6

Row: 6

B: numeric input
4.5

C: formula
=FACT(B6)

C: expected result
24

Row: 7

B: numeric input
5

C: formula
=FACT(B7)

C: expected result
120

Row: 8

B: numeric input
6

C: formula
=FACT(B8)

C: expected result
720

Row: 9

B: numeric input
7

C: formula
=FACT(B9)

C: expected result
5,040

Row: 10

B: numeric input
10

C: formula
=FACT(B10)

C: expected result
3,628,800

To test the invalid case independently, enter =FACT(-1) in an extra result cell outside the table. The official guide treats negative arguments as invalid, so expect a calculation error, not a particular string such as Excel’s error identifiers. Keep this diagnostic separate from the valid row dataset. For zero, explain 0! = 1 as a standard factorial definition rather than a special cell-format rule ([A1], [M1]).

Count ordered selections without replacement

If five distinguishable objects are available and you select an ordered group of three without replacement, the count is 5×4×3 = 60. A factorial approach uses =FACT(5)/FACT(5-3) with independent expected result 60 (120÷2). In a separate table named SelectionCounts with total items in B2=5 and selected slots in C2=3, the parameterized formula is =FACT(B2)/FACT(B2-C2). This is valid only for whole-number counts 0 ≤ C2 ≤ B2 and counts distinct items; it does not allow a fractional or negative inventory.

Count unordered combinations

For five distinguishable items, choosing three regardless of order gives 5!/(3!×2!) = 10. Enter =FACT(5)/(FACT(3)*FACT(5-3)); the expected result is 10 by independent arithmetic ([M1]). In that SelectionCounts table, use =FACT(B2)/(FACT(C2)*FACT(B2-C2)) for numeric B2=5 and C2=3. For large counts, factorial intermediates can exceed numeric limits even when the final combinatorial count is not extreme; native threshold and rounding behavior remain untested.

Decimal inputs can disguise data-quality problems

Because the Apple function drops the fractional part of its argument, =FACT(4.5) evaluates like =FACT(4) and yields 24. This is correct documented behavior, but a person counting physical objects should normally enter an integer: 4.5 items may indicate a data-entry error. A review column can use =B2=INT(B2) to check whether a nonnegative numeric input is whole-valued. The INT function has separate official documentation and sign-specific rules; this quality check should not be treated as proof the value is in the allowable FACT domain. Another cell, =B2>=0, checks one part of the domain. For an imported sheet, validate both type and whole-number status explicitly.

FACT is not FACTDOUBLE

Apple documents FACTDOUBLE separately: it multiplies every second descending integer, rather than every integer. For instance, 5!! = 5×3×1 = 15 by mathematical definition, while FACT(5) = 120. Do not interchange the names when reproducing formulas from another product or from a research paper; see the official FACTDOUBLE page ([R1-FACTDOUBLE]).

Table and sheet references

In FactorialPractice, B2 is sufficient when C2 is in the same table. If a result is in another table, use the editor to select the cell and insert a qualified token such as FactorialPractice::B2; on a different sheet the formula editor can include the sheet as well. References are normally relative when filled down; the source row must move with the result row ([A4]).

This tutorial does not certify the exact Apple Numbers error string, behavior on Boolean/date/duration input, behavior on quoted numeric text, integer overflow limits, or internal floating-point precision. The Apple reference establishes the listed numeric behavior, not every native-app coercion and error state. Errors mentioned here are documented mathematical/domain conditions or troubleshooting hypotheses, not screenshots or runtime observations.

The named function also appears in Microsoft Excel and Google Sheets, with matching basic mathematical intent for the documented cases. This does not establish identical date/duration coercion, localized function names, precise overflow thresholds, display formatting, empty-cell treatment, or native error strings. In particular, moving formulas between Numbers and Excel/Sheets can require changing table/sheet references and locale-specific argument separators. Check any workbook after import, rather than assuming formula parity implies application parity ([X1], [X2]).

• Microsoft Excel — FACT function
• Google Sheets — FACT function

• FACTDOUBLE — official function documentation
• MULTINOMIAL — official function documentation

• FACTDOUBLE — 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 FACT, Apache OpenOffice Calc FACT, Gnumeric FACT. 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.