MOD function

MOD returns what is left over after one number is divided by another. MOD(10,3) is 1, because 3 goes into 10 three times with 1 remaining.

It is the function for anything cyclical. Odd and even rows, every fifth line, the day of a repeating schedule, the cents left over after splitting a bill: each is a remainder.

Paired with INT, which gives the number of whole divisions, MOD gives you a complete picture of a division with no decimals.

Two practical notes. First, the divisor is the cycle length, and the answer runs from 0 up to one less than the divisor. A zero-based cycle of 7 gives 0 to 6, so add 1 when you want 1 to 7. Second, MOD is exact on whole numbers but can show tiny errors on decimals, which matters if you test the result against 0. For money, work in cents or round the inputs first.

Outside tasks, MOD is how timetables repeat, how check digits are calculated, and how a long list is dealt into teams one row at a time.

A handy fact: MOD(n,1) returns the decimal part of a positive number, and MOD(n,10) the last digit. Both are quick ways to peel numbers apart.

Because MOD works on the sign of the divisor, MOD(-1,7) is 6, which is useful when you want a count to wrap backward around a week or a schedule. Spreadsheets that rotate a roster use exactly this: subtract a number of days, then wrap the result with MOD so it never goes below zero.

Remainder tasks come in three flavors. Leftover items after packing: MOD(47,12). Alternating rows: shade every other row with the conditional formatting rule =MOD(ROW(),2)=0. Rotation: assign people to four teams in turn with =MOD(ROW()-2,4)+1 copied down from row 2.

If the task wants both the number of full groups and the leftover, INT and MOD are the matched pair. Check one row by hand to confirm the remainder before filling down.