Division with remainder splits a division into a whole-number quotient and a leftover remainder. They always satisfy a = q × b + r, where a is the dividend, b the divisor, q the quotient and r the remainder. This calculator returns both, checks divisibility, and shows the decimal result.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: integer division identity, recomputed in code.
The identity
The quotient is how many whole times the divisor fits into the dividend; the remainder is what's left. For positive numbers the remainder is always between 0 and one less than the divisor. A remainder of 0 means the division is exact and the divisor is a factor. This calculator truncates toward zero, so a negative dividend gives a remainder with the same sign — matching the modulo operator in most programming languages.
Worked examples
100 ÷ 7:
25 ÷ 5 (exact):
7 ÷ 10 (small dividend):
Each result can be checked with the identity: 14 × 7 + 2 = 100, 5 × 5 + 0 = 25, and 0 × 10 + 7 = 7. That a = q × b + r check is exactly what the calculator displays.
Frequently Asked Questions
Quotient = whole times b fits into a; remainder = what's left. a = q×b + r. 17 ÷ 5 → q 3, r 2.
14 remainder 2: 14 × 7 = 98, 100 − 98 = 2.
Exact division — the divisor is a factor. 25 ÷ 5 = 5 r 0.
For positives, yes (a mod b). With truncated division, negatives give a remainder signed like the dividend.
Quotient 0, remainder = a. 7 ÷ 10 → q 0, r 7.