Modulo Calculator (a mod n)
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Modulo Calculator (a mod n) by TheCalcTools
How the Modulo Calculator (a mod n) works
The modulo is what is left after division. For positive numbers both conventions agree. With a negative number they differ: the floored version (used in mathematics and Python) gives a result with the sign of the modulus; the truncated version (C, Java, JavaScript %) gives the sign of the dividend.
Clock arithmetic is mod 12 (or 24): 15:00 is 3 o’clock because 15 mod 12 = 3.
The formula
Worked example
Using the default values shown in the calculator:
| Number (a) | -17 |
|---|---|
| Modulus (n) | 5 |
- −17 mod 5 = 3.0000 (floored); −17 % 5 = -2.0000 (truncated).
Result:
| a mod n (floored, always the sign of n) | 3.0000 |
|---|---|
| Remainder a % n (truncated, sign of a) | -2.0000 |
| Floored quotient | -4 |
| Truncated quotient | -3 |
| Congruence | -17 ≡ 3 (mod 5) |
Frequently asked questions
What is −17 mod 5?
3 with the floored (mathematical) definition, and −2 with the truncated definition used by % in C and JavaScript.
Sources and further reading
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