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What is the mathematical term and symbol for division without remainders?

Take for example 322 / 100.

I know 322 / 100 is division and the result is 3.22. I know 322 % 100 is a modulo and the result is 22.

But what is the proper term and symbol for division with no remainder?

Eg, 322 SYMBOL 100 would give 3.

mikemaccana
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    You could do $\lfloor 322/100\rfloor$ – kiyomi Mar 02 '21 at 11:02
  • One way would be to use the div operator: 322 div 100 = 3. – Artur Wiadrowski Mar 02 '21 at 11:03
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    A commonly used term is "integer division" (or in some contexts, just "division", but that is rarer). – preferred_anon Mar 02 '21 at 11:06
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    BTW, % is not commonly used in mathematics as an operator to denote modulus division. In programming, it is used in many languages which have inherited (or borrowed) it from C, but there are many exceptions (not just in languages older than C). See https://en.wikipedia.org/wiki/Modulo_operation#In_programming_languages – PM 2Ring Mar 02 '21 at 11:33
  • Thanks @preferred_anon. Knowing the term 'integer division' was critical to being able to search for the topic in my programming language (and know what the preferred way to do integer division in that language is). – mikemaccana Mar 02 '21 at 12:53
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    FWIW, in Python, there's a floor division operator, //. See https://docs.python.org/3/reference/expressions.html#binary-arithmetic-operations & https://docs.python.org/3/library/stdtypes.html#numeric-types-int-float-complex – PM 2Ring Mar 04 '21 at 06:14

1 Answers1

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The term is 'integer division'. The symbol used is $\lfloor \frac{322}{100} \rfloor$ or sometimes $[\frac{322}{100}]$ and $100\,|\,300$ if one is a divisor of the other.

mikemaccana
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Marius S.L.
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    I would strongly advise against using $100\mid 300$, because as far as I know it's way more common to find it referred to the statement that there is an integer $k$ such that $300=100k$, rather than to the number $3$ itself. –  Mar 02 '21 at 11:07
  • That's why I wrote "if one is a divisor of the other"! – Marius S.L. Mar 02 '21 at 11:09
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    It can't hurt to specify the nuance of what's a function and what's a statement. –  Mar 02 '21 at 11:12
  • $100,|,300$ is a symbol for a division without remainder - as asked. This is an academic discussion based on a question which can be read either way. – Marius S.L. Mar 02 '21 at 11:28
  • I added the term to this answer - hope that's OK. – mikemaccana Mar 02 '21 at 12:51