FACT in Excel: Factorials, Distinct Arrangements and Integer Inputs

• Introduced: First introduction version is not established by the official history reviewed.
• Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026; official FACT reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=FACT(number)

The argument is required. Microsoft specifies a nonnegative input and truncates a noninteger number before computing its factorial. Its examples explicitly give FACT(0)=1 and a #NUM! error for FACT(−1).

English names, comma separators and decimal points are used below. Truncation is a documented calculation rule, not permission to accept fractional counts in a model where an item cannot be divided. Validate the source before interpreting an arrangement count.

Enter 0, 1, 2, 3, 4, 5, 6 in A2:A8. Fill =FACT(A2) down in B2:B8.

Expected results are 1, 1, 2, 6, 24, 120, 720. The zero result is one, not zero: there is one empty arrangement when no objects are selected. Multiplying the running product by a zero factor would incorrectly erase every later factorial.

For a noninteger control, =FACT(6.9) has expected result 720, because the documented truncation selects 6. This is not FACT(7), and it is not a continuous interpolation between two factorials.

Four different display cards A, B, C and D can occupy four positions. There are four choices for the first position, then three, two and one:

=FACT(4)
=4*3*2*1

Both expected results are 24. ABCD and BACD are different orders. If order does not matter and all four cards are simply selected together, there is only one selected set, so factorials would answer the wrong question.

For six distinct cards, fill three different ordered slots without replacement:

=FACT(6)/FACT(6-3)

Expected count: 120, agreeing with 6×5×4. The remaining three cards are not assigned positions, so their possible orders should not be counted. Dividing by FACT(3) removes those unused arrangements.

For an unordered three-card selection, COMBIN instead gives 20. Each selected group has six possible internal orders, explaining the factor-of-six difference. Keep order and replacement rules in the problem statement.

For the four-character multiset A, A, B, C, swapping the two identical A labels does not create a visibly new sequence:

=FACT(4)/FACT(2)

Expected distinct sequence count: 12. Treating both A labels as different would give 24 and double-count each visible outcome. MULTINOMIAL expresses this repeated-label count directly with counts 2, 1 and 1.

The division applies because the two A copies are indistinguishable for the stated report. If they have separate serial numbers and identity matters, the original distinct-object count would be appropriate instead.

Use nonnegative whole counts for the model. The direct reference supplies the negative-input #NUM! example, but it does not establish every nonnumeric coercion, fractional-negative ordering or maximum representable factorial.

Factorials grow quickly. A ratio can be mathematically modest while separately computing its numerator and denominator creates unnecessarily large intermediates. Prefer a dedicated combination function for that question and do not treat a displayed integer as proof of exact native arithmetic at every magnitude.

• Microsoft FACT reference.
• Editorial testing standards.

Worked inputs are fictional. Decimal answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.