Check ISNUMBER and an integer condition before testing parity. Keep input problems visible instead of labeling them even.
In Google Sheets, =ISODD(A2) is convenient when A2 already contains an integer. For a shared sheet or an imported column, check the input first. A useful classification column should distinguish an even integer from a fraction, text, or a broken formula.
Build a classification column
=IFERROR(IF(ISNUMBER(A2),IF(A2=INT(A2),MOD(A2,2)<>0,"Not an integer"),"Not a number"),"Input error")
Enter the formula in B2 and fill it down for the records you want to inspect. Numeric whole values receive TRUE or FALSE. Fractions receive Not an integer. Text and blank cells receive Not a number. The outer IFERROR gives an explicit result when an error reaches the calculation.
Validate stored types and whole values
ISNUMBER checks the stored value's type, not merely whether its displayed characters resemble digits. Google documents that a string such as "123" fails the check in its ISNUMBER reference. That behavior is helpful when an import has left some rows as text and other rows as numbers.
The equality with INT(A2) tests whether the original numeric value is whole. It rejects both 7.25 and -7.25. Only after that validation does the remainder expression classify the number. This makes the worksheet's input policy explicit instead of relying on a parity function to validate fractions.
Google's MOD documentation describes the remainder calculation. With a positive divisor of two, both positive and negative odd integers have nonzero results. Test -11, -10, 0, 10, and 11: the first and last values should return TRUE.
Once the numeric column is validated, the shorter ISODD expression is easy to read. Its function reference describes the logical result. Keep the longer validation formula wherever newly entered values still need review; parity and whole-number validation are separate responsibilities.
Highlight rows containing odd integers
You can also highlight qualifying rows using a custom conditional-formatting formula. For a range starting on row two and values in column A, use:
=IFERROR(AND(ISNUMBER($A2),$A2=INT($A2),MOD($A2,2)<>0),FALSE)
The dollar sign fixes column A while leaving the row relative to each formatted record. The formula returns false for invalid input, so conditional formatting does not paint an erroneous row as odd. Keep the classification column too if people need to see why a row was excluded.
Separate cell values from row positions
These rules inspect cell values, not the parity of row positions. If the task is alternating background colors, use a row-based rule instead. Sorting, inserting rows, and filtering can change positions while leaving the stored number unchanged. Decide which of those two questions the sheet should answer before choosing its formula.