FACT in Zoho Sheet: Factorials, Arrangements and Combinations

=FACT(number)

The Zoho FACT documentation explicitly shows =FACT(5.3) → 120, =FACT(0.44) → 1, and =FACT(10) → 3,628,800. These are vendor examples, independent of our own arithmetic. The article does not publish a guaranteed maximum finite argument, precise behavior for all negative values, or a first-supported product version. For real-world counting, validate that the input is a nonnegative integer before applying this function, even though the documented function truncates positive decimals.

A factorial can also be described mathematically as the product of all positive integers from 1 through n, with 0!=1. It is only this nonnegative-integer factorial that the guide uses as a guaranteed mathematical model. Advanced extensions of factorials to nonintegers using the Gamma function are a different subject and should not be inferred as Zoho FACT features.

Enter the factorial inputs below in E2:E9, with Factorial input in E1. Enter =FACT(E2) in G2 and fill through G9 after verifying the import uses numeric values in column E. These are expected independent mathematical results, not saved screenshots or outputs from the Zoho application.

Step by step: Begin with a small value that can be audited by multiplication, such as 3. Calculate 3×2×1=6 on paper. Enter the formula in the appropriate row. Copy it down while retaining the relative E-row references. Then check the vendor decimal example: E5 is 5.3, and the documented truncation makes the mathematical expected result 120, not a rounded-up six factorial of 720. If you are importing real-world counts from text or a database, explicitly convert and validate them first rather than using FACT’s implicit truncation to hide bad data.

A display must show six distinct art prints in a row. How many different orders can those six prints appear in, assuming each appears exactly once? The first position has six choices, then five, then four, and so on. Type:

=FACT(6)

The expected number of distinct lineups is 720. If three of the six distinct prints are chosen and the order of those three matters, the mathematical number of arrangements is 6×5×4=120, represented with factorials by:

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

The numerator counts all complete six-item arrangements, and dividing by 3! cancels arrangements of the unchosen three items. The expected result is 120. This formula has not been executed inside Zoho. The related PERMUT function may express the problem more directly, but consult its separate official documentation before substituting syntax.

Suppose eight distinct volunteers are available and three are chosen for a team; any ordering of the same three volunteers counts as one team. Divide the arrangement count by the number of ways to permute the selected three:

=FACT(8)/(FACT(3)*FACT(8-3))

The independently expected result is 56. You can manually verify the numerator is 40,320 and the denominator is 6×120=720; 40320/720=56. This is the binomial coefficient “8 choose 3.” Zoho separately documents COMBIN, but a similar function name is not enough to assert identical edge handling across products or versions. Use nonnegative whole numbers with 0≤selected≤available and check against the business definition before applying the formula.

Large arrangements or selection counts can exceed a spreadsheet’s usable exact numerical range before they reach a truly infinite mathematical value. A mathematical answer computed with Python arbitrary-precision integers is not proof that a floating-point spreadsheet can store every digit of the answer.

Before putting factorials into reporting, add an explicit data-quality step that confirms counts are whole and nonnegative. An illustrative formula such as =IF(AND(E2>=0;E2=INT(E2));FACT(E2);"Check count") expresses that policy using related functions; its combined native execution has not been tested in this batch. Always assess whether the source contains blanks, strings or locale-specific decimal formatting.

Microsoft’s FACT reference documents factorial syntax, fractional-input truncation and #NUM! for Excel’s negative inputs. This independently confirms an Excel-specific behavior. Zoho’s retrieved article documents some of the same positive examples but does not establish every Excel error/precision limit for Zoho. Google Sheets may provide a like-named factorial function; validate its exact coercion and error rules separately rather than presuming universal equivalence.

Zoho’s 2026 desktop beta announcement indicates 400+ desktop functions while noting that some web features remain under development. This guide cannot establish identical FACT behavior for every account, platform or release, and does not invent a function-introduction date.

Zoho help checked: October 11, 2026. Independent calculation: Python integer factorial and exact combinatorial arithmetic, plus manually inspectable products. Native Zoho Sheet tests: none (0). Screenshot evidence: none. Read the primary Zoho FACT article and the related FACTDOUBLE and COMBIN guides for different counting problems.