# Quotient vs. Modulo

## Difference Between Quotient and Modulo

#### Quotient➦

In arithmetic, a quotient (from Latin: quotiens "how many times", pronounced ) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division (in the case of Euclidean division), or as a fraction or a ratio (in the case of proper division).

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#### Modulo➦

(Mathematics) With respect to a specified modulus

18 is congruent to 42 modulo 12 because both 18 and 42 leave 6 as a remainder when divided by 12.

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#### Quotient➦

The number obtained by dividing one quantity by another. In 45 ÷ 3 = 15, 15 is the quotient.

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#### Modulo➦

Correcting or adjusting for something, as by leaving something out of account

This proposal is the best so far, modulo the fact that parts of it need modification.

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#### Quotient➦

(arithmetic) The number resulting from the division of one number by another.

The quotient of 12 divided by 4 is 3.

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#### Modulo➦

(mathematics) Given a specified modulus of.

21 and 84 are congruent to each other modulo 9, since both numbers leave the same remainder, 3, when divided by 9.

Thus 21 modulo 9 is 3, because when 21 is divided by 9, the remainder is 3.

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#### Quotient➦

(arithmetic) The integer part of the result of such division.

The quotient of 13 divided by 4 is 3, and the remainder is 1.

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#### Modulo➦

(technical) Except for differences accounted for by.

"A is the same as B modulo C" means A is the same as B except for differences accounted for by C.

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#### Quotient➦

(mathematics) By analogy, the result of any process that is the inverse of multiplication as defined for any mathematical entities other than numbers.

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#### Modulo➦

(extended use) With due allowance for (a specified exception or particular detail).

In the Lisp programming language, the "tail recursion modulo cons" technique allows functions that would be tail recursive but for a cons call to be transformed into a tail recursive form.

All mammals, modulo the monotremes, give birth to live young.

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#### Quotient➦

A quotum or quota.

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#### Modulo➦

(computing) The operation or function that returns the remainder of one number divided by another.

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#### Quotient➦

The number resulting from the division of one number by another, and showing how often a less number is contained in a greater; thus, the quotient of twelve divided by four is three.

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#### Quotient➦

The result of any process inverse to multiplication. See the Note under Multiplication.

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#### Quotient➦

the ratio of two quantities to be divided

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#### Quotient➦

the number obtained by division

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