A remainder is what is left after division into whole groups. 17 divided by 5 is 3 remainder 2, because 5 × 3 = 15 and 2 is left. You can also write 17 = 5q + r with 0 ≤ r < 5. Integers around this are in integers on ACT Math.
What the remainder cannot be
When you divide by 5, the remainder is 0, 1, 2, 3, or 4. A remainder of 5 would have been another full group. Factors and multiples, which is remainder 0, are in factors, multiples, LCM, and GCF.
Consecutive integers often rotate through remainders. Three consecutive numbers divided by 3 leave remainders 0, 1, and 2 in some order, in consecutive integers. Odd and even are remainders of 1 or 0 when you divide by 2, in odd, even, positive, and negative.
The bottom line
Write n = divisor × quotient + remainder, and keep the remainder smaller than the divisor.
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