プラン

剰余の計算機 (a mod n)

この計算機は a mod n、つまり a を n で割った余りを、負の数を含むどんな整数についても求めます。商、引き算、そして数学の答えと一部のプログラミング言語の % 演算子との違いを示します。

結果

値を入力して「計算」を押すと結果が表示されます。

公式

a mod n=a−n⌊an⌋a \bmod n = a - n \left\lfloor \frac{a}{n} \right\rfloor

Divide, round down to a whole number, multiply back and subtract. For n > 0 the answer is between 0 and n − 1.

この計算ツールの使い方

  1. Enter the number a and the modulus n (whole numbers; n cannot be 0).
  2. Press Calculate to see a mod n, the quotient and each step.

解き方付き例題

17 mod 5

17 ÷ 5 = 3.4, which rounds down to 3.

17 − 5 × 3 = 2, so 17 mod 5 = 2.

−17 mod 5 (a negative number)

−17 ÷ 5 = −3.4, which rounds down to −4.

−17 − 5 × (−4) = 3, so −17 mod 5 = 3. (The % operator in C or JavaScript gives −2.)

100 mod 7

100 ÷ 7 = 14.28…, so the quotient is 14.

100 − 7 × 14 = 2.

よくある間違い

  • Giving the quotient instead of the remainder: 17 mod 5 is 2, not 3.
  • Rounding −3.4 to −3 instead of down to −4 for negative numbers.
  • Expecting the same answer from % in every programming language; they differ for negatives.

よくある質問

What does mod mean in math?

a mod n is the remainder when a is divided by n. For example 17 mod 5 = 2, because 17 = 3 × 5 + 2.

How do you calculate mod of a negative number?

Divide and round down (towards negative infinity), then subtract. −17 mod 5: −17 ÷ 5 = −3.4 → −4, and −17 − 5 × (−4) = 3.

Where is modulo used?

Clock arithmetic (14:00 is 2 pm because 14 mod 12 = 2), checking whether a number is even (n mod 2), check digits, and programming.