# Quotient vs. Factor — What's the Difference?

By Tayyaba Rehman — Updated on August 25, 2023
A quotient is the result of division, while a factor is a number that divides another without leaving a remainder.

## Key Differences

A quotient is fundamentally associated with the arithmetic operation of division. When one number is divided by another, the resulting value is termed the quotient. In contrast, the term factor refers to a number that can be multiplied with another to yield a specified product.
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Aug 25, 2023
For instance, when 20 is divided by 5, the quotient is 4. In the context of factors, 5 and 4 are both factors of 20 since 5 multiplied by 4 gives 20. Therefore, while quotient is an outcome of division, a factor is inherently linked to multiplication.
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Aug 25, 2023
It's crucial to understand the difference in application between quotient and factor in mathematical problems. Determining the quotient is essential in scenarios requiring equal distribution, while identifying factors can be pivotal in understanding the divisible properties of a number.
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Aug 25, 2023
One can recognize factors as foundational building blocks of numbers. Every number has at least two factors: 1 and the number itself. The quotient, on the other hand, offers insight into the divisible nature of numbers in relation to each other.
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Aug 25, 2023
Mathematically, both quotient and factor are vital concepts, each serving unique purposes. The quotient helps discern distribution properties, and the factor aids in breaking down numbers into their elementary components.
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Aug 25, 2023

## Comparison Chart

### Basic Definition

Result of division
Number that divides another without leaving a remainder
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Division
Multiplication
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### Example

In 12 ÷ 4, 3 is the quotient
In 12, 1, 2, 3, 4, 6, and 12 are factors
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### Application

Understanding equal distribution
Understanding divisible properties of a number
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### Mathematical Significance

Provides insight into divisible relations of numbers
Breaks down numbers into foundational components
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## Compare with Definitions

#### Quotient

Result when one number is divided by another.
When 15 is divided by 3, the quotient is 5.
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#### Factor

A number that divides another number exactly.
5 is a factor of 20.
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#### Quotient

Outcome of a division in mathematical terms.
In the fraction 7/2, the whole number quotient is 3 with a remainder of 1.
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#### Factor

One of two or more quantities that multiply together to give a product.
3 and 4 are factors of 12.
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#### Quotient

The answer to a division problem.
The teacher asked the students to find the quotient of 25 divided by 5.
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#### Factor

An element or cause that brings about a result.
Weather is a significant factor in crop yields.
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#### Quotient

Value obtained from the division operation.
The quotient of 8 divided by 2 is 4.
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#### Factor

A circumstance, fact, or influence that contributes to a result
His skill was a factor in ensuring that so much was achieved
She worked fast, conscious of the time factor
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#### Quotient

A measure or degree of a specified quality or characteristic.
The intelligence quotient of an individual can be determined through specific tests.
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#### Factor

An agent who buys and sells goods on commission
His father was chief factor for the Hudson's Bay Company
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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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#### Factor

Another term for factorize
Last year researchers factored a number 155 digits long
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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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#### Factor

(obsolete) A doer, maker; a person who does things for another person or organization.
The factor of the trading post bought the furs.
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#### Quotient

A quotum or quota.
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#### Factor

To sell a debt or debts to an agent (the factor) to collect.
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#### 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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#### Factor

Any of a number of substances in the blood, mostly identified by numerals, which are involved in coagulation.
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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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#### Factor

(Mathematics) One of two or more quantities that divides a given quantity without a remainder. For example, 2 and 3 are factors of 6; a and b are factors of ab.
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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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#### Factor

To engage in purchasing accounts receivable at a discount.
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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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#### Factor

A commission agent.
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#### Quotient

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

To be a product of other objects.
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#### Quotient

The ratio of two quantities to be divided
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#### Factor

A steward or bailiff of an estate.
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#### Quotient

The number obtained by division
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#### Factor

One of the elements or quantities which, when multiplied together, form a product.
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#### Factor

To resolve (a quantity) into its factors.
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#### Factor

A number or quantity that when multiplied with another produces a given number or expression
An amount that exceeds it by a factor of 1000 or more
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#### Factor

A level on a scale of measurement.
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#### Factor

(of a company) sell (its invoices) to a factor
They collected rents while he factored these forfeited estates
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#### Factor

One that actively contributes to an accomplishment, result, or process
"Surprise is the greatest factor in war" (Tom Clancy).
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#### Factor

One who acts for someone else; an agent.
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#### Factor

One who purchases accounts receivable at a discount.
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#### Factor

A quantity by which a stated quantity is multiplied or divided, so as to indicate an increase or decrease in a measurement
The rate increased by a factor of ten.
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#### Factor

A gene. No longer in technical usage.
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#### Factor

(Physiology) A substance that functions in a specific biochemical reaction or bodily process, such as blood coagulation.
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#### Factor

To determine or indicate explicitly the factors of
If you factor 70, you get 2, 5, and 7.
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#### Factor

An agent or representative.
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#### Factor

A person or business organization that provides money for another's new business venture; one who finances another's business.
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#### Factor

A business organization that lends money on accounts receivable or buys and collects accounts receivable.
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#### Factor

One of the elements, circumstances, or influences which contribute to produce a result.
The greatest factor in the decision was the need for public transportation.
The economy was a factor in this year's budget figures.
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#### Factor

(mathematics) Any of various objects multiplied together to form some whole.
3 is a factor of 12, as are 2, 4 and 6.
The factors of the Klein four-group are both cyclic of order 2.
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#### Factor

(causal analysis) Influence; a phenomenon that affects the nature, the magnitude, and/or the timing of a consequence.
The launch temperature was a factor of the Challenger disaster.
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#### Factor

(economics) A resource used in the production of goods or services, a factor of production.
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#### Factor

(Scotland) A steward or bailiff of an estate.
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#### Factor

(transitive) To find all the factors of (a number or other mathematical object) (the objects that divide it evenly).
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#### Factor

One who transacts business for another; an agent; a substitute; especially, a mercantile agent who buys and sells goods and transacts business for others in commission; a commission merchant or consignee. He may be a home factor or a foreign factor. He may buy and sell in his own name, and he is intrusted with the possession and control of the goods; and in these respects he differs from a broker.
My factor sends me word, a merchant's fledThat owes me for a hundred tun of wine.
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#### Factor

One of the elements, circumstances, or influences which contribute to produce a result; a constituent; a contributory cause.
The materal and dynamical factors of nutrition.
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#### Factor

Anything that contributes causally to a result;
A number of factors determined the outcome
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#### Factor

An abstract part of something;
Jealousy was a component of his character
Two constituents of a musical composition are melody and harmony
The grammatical elements of a sentence
A key factor in her success
Humor: an effective ingredient of a speech
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#### Factor

Any of the numbers (or symbols) that form a product when multiplied together
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#### Factor

One of two or more integers that can be exactly divided into another integer;
What are the 4 factors of 6?
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#### Factor

A businessman who buys or sells for another in exchange for a commission
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#### Factor

An independent variable in statistics
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#### Factor

(genetics) a segment of DNA that is involved in producing a polypeptide chain; it can include regions preceding and following the coding DNA as well as introns between the exons; it is considered a unit of heredity;
Genes were formerly called factors
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#### Factor

Resolve into factors;
A quantum computer can factor the number 15
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#### Factor

A circumstance, fact, or influence contributing to a result.
Diet is an important factor in maintaining good health.
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#### Factor

Something that plays a role in achieving an outcome.
Skill was a major factor in his success.
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## Common Curiosities

#### What is the primary function of a quotient in division?

The quotient represents the result or outcome of a division operation.
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#### Can a quotient be a decimal?

Yes, when dividing two numbers, the quotient can be a whole number, fraction, or decimal.
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#### Can any number be a factor of another number?

No, a factor must divide another number exactly without leaving a remainder.
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#### How is the quotient different from the remainder in division?

The quotient is the result of division, while the remainder is what's left over when one number can't be divided evenly by another.
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#### Are 1 and the number itself always factors of the number?

Yes, 1 and the number itself are always factors of that number.
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#### Do factors always exist for non-prime numbers?

Yes, non-prime numbers have factors other than 1 and themselves.
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#### What is the difference between a prime and composite number regarding factors?

A prime number has only two factors, 1 and itself, while a composite number has more than two factors.
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#### If I know the factors of a number, can I determine the number?

Yes, by multiplying two factors, you can determine the original number.
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#### How is the quotient used outside of mathematics?

Terms like "intelligence quotient" use the concept to measure specific qualities or characteristics.
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#### Does every division operation yield a quotient?

Yes, every division operation results in a quotient, which might be a whole number, fraction, or decimal.
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