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Factor vs. Product — What's the Difference?

By Maham Liaqat & Fiza Rafique — Updated on May 15, 2024
In mathematics, a factor is a number that divides another without leaving a remainder, whereas a product is the result of multiplying two or more factors.
Factor vs. Product — What's the Difference?

Difference Between Factor and Product

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Key Differences

Factors are integers that divide another integer completely, contributing to the composition of a number, whereas products result from the multiplication of two or more numbers, representing the outcome of an arithmetic operation.
In the context of multiplication, factors are the numbers being multiplied together, on the other hand, the product is the total or sum obtained after the multiplication process is completed.
Factors can be considered the building blocks of a number, as they are the numbers that, when multiplied together, reproduce the original number, while products are seen as the creation or result of combining these building blocks.
While finding factors is essential for simplifying algebraic expressions or solving integer problems, finding products is crucial in operations involving scaling, area calculations, and other applications needing multiplication.
Factors are used in various mathematical disciplines such as number theory, where the focus is on divisibility and the properties of integers, whereas products are used more broadly in everyday mathematics, including finance, engineering, and physics.
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Comparison Chart

Definition

A number that divides another number without leaving a remainder.
The result of multiplying two or more numbers.

Role in Arithmetic

Integral part of a number.
Outcome of multiplication.

Key Operation

Division (to find factors).
Multiplication (to find product).

Importance in Mathematics

Essential for divisibility, factors of numbers.
Essential in basic arithmetic, algebra.

Example

3 is a factor of 12.
12 is the product of 3 and 4.

Compare with Definitions

Factor

A divisor of a number.
2 is a factor of 10 because 10 divided by 2 equals 5.

Product

Can be visualized in area calculation.
The area of a 7x5 rectangle is the product, 35 square units.

Factor

Used in breaking down numbers.
The factors of 6 are 1, 2, 3, and 6.

Product

Key in exponential growth calculations.
Doubling every day, the product of growth over three days is 8.

Factor

Essential in algebra for solving equations.
Factoring x^2 - 9 gives (x - 3)(x + 3).

Product

Used in algebra for expanding.
The product of (x - 2)(x + 2) is x^2 - 4.

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

Product

An item that is made or refined and marketed
Farm products.
Soaps, detergents, and similar products.
Travel products such as vacation trips.

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

Product

Such items considered as a group
Sold a lot of product in May.

Factor

A level on a scale of measurement.

Product

A preparation, such as a gel, used for styling hair
Began to use product soon after he became famous.

Factor

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

Product

A substance resulting from a chemical or nuclear reaction.

Factor

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

Product

A direct result; a consequence
"Is history the product of impersonal social and economic forces?" (Anthony Lewis).

Factor

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

Product

A person whose characteristics or abilities are the result of certain influences or kinds of experience
"She is the product of an America in which explicit displays of pride in intellect are considered unseemly" (Yuval Levin).

Factor

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

Product

The number or quantity obtained by multiplying two or more numbers together.

Factor

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

Product

A scalar product.

Factor

One who acts for someone else; an agent.

Product

A vector product.

Factor

One who purchases accounts receivable at a discount.

Product

Anything that is produced; a result.
The product of last month's quality standards committee is quite good, even though the process was flawed.

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.

Product

The amount of an artifact that has been created by someone or some process.
They improve their product every year; they export most of their agricultural production.

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.

Product

A consequence of someone's efforts or of a particular set of circumstances.
Skill is the product of hours of practice.
His reaction was the product of hunger and fatigue.

Factor

A gene. No longer in technical usage.

Product

(chemistry) A chemical substance formed as a result of a chemical reaction.
This is a product of lime and nitric acid.

Factor

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

Product

(arithmetic) A quantity obtained by multiplication of two or more numbers.
The product of 2 and 3 is 6.
The product of 2, 3, and 4 is 24.

Factor

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

Product

(mathematics) Any operation or a result thereof which generalises multiplication of numbers, like the multiplicative operation in a ring, product of types or a categorical product.

Factor

To engage in purchasing accounts receivable at a discount.

Product

Any tangible or intangible good or service that is a result of a process and that is intended for delivery to a customer or end user.

Factor

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

Product

A commodity offered for sale.
That store offers a variety of products.
We've got to sell a lot of product by the end of the month.

Factor

An agent or representative.

Product

Any preparation to be applied to the hair, skin, nails, etc.
Wash excess product out of your hair.

Factor

(legal)

Product

Illegal drugs, especially cocaine, when viewed as a commodity.
I got some product here – you buying?

Factor

A commission agent.

Product

To produce.

Factor

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

Product

Anything that is produced, whether as the result of generation, growth, labor, or thought, or by the operation of involuntary causes; as, the products of the season, or of the farm; the products of manufactures; the products of the brain.
There are the productOf those ill-mated marriages.
These institutions are the products of enthusiasm.

Factor

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

Product

The number or sum obtained by adding one number or quantity to itself as many times as there are units in another number; the number resulting from the multiplication of two or more numbers; as, the product of the multiplication of 7 by 5 is 35. In general, the result of any kind of multiplication. See the Note under Multiplication.

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.

Product

To produce; to bring forward.

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.

Product

To lengthen out; to extend.
He that doth much . . . products his mortality.

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.

Product

To produce; to make.

Factor

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

Product

Commodities offered for sale;
Good business depends on having good merchandise
That store offers a variety of products

Factor

(Scotland) A steward or bailiff of an estate.

Product

An artifact that has been created by someone or some process;
They improve their product every year
They export most of their agricultural production

Factor

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

Product

A consequence of someone's efforts or of a particular set of circumstances;
Skill is the product of hours of practice
His reaction was the product of hunger and fatigue

Factor

To be a product of other objects.

Product

A chemical substance formed as a result of a chemical reaction;
A product of lime and nitric acid

Factor

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

Product

A quantity obtained by multiplication;
The product of 2 and 3 is 6

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.

Product

The set of elements common to two or more sets;
The set of red hats is the intersection of the set of hats and the set of red things

Factor

A steward or bailiff of an estate.

Product

Result of multiplication.
The product of 5 and 4 is 20.

Factor

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

Product

Common in financial calculations.
Total cost is the product of unit price and quantity.

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.

Factor

To resolve (a quantity) into its factors.

Factor

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

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

Factor

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

Factor

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

Factor

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

Factor

An independent variable in statistics

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

Factor

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

Factor

Integral in finding prime numbers.
Prime factors of 30 are 2, 3, and 5.

Factor

Helps in simplifying fractions.
15 and 45 share common factors, simplifying their ratio.

Common Curiosities

What is a factor in mathematics?

A factor is a number that divides another number completely without leaving a remainder.

What is a product in mathematics?

A product is the result of multiplying two or more numbers together.

Can the product of two numbers be less than both of them?

Yes, when both numbers are fractions less than 1.

How do factors and products relate to each other?

Factors are numbers that, when multiplied (product), reproduce the original number.

Why is factoring important?

Factoring is crucial for simplifying expressions and solving equations in mathematics.

What's an example of a product in real life?

Calculating the total cost in shopping by multiplying the quantity by the price per item.

How are products used in algebra?

Products are used in expanding expressions and solving polynomial equations.

What tools help in finding factors?

Factoring trees, division, and prime factorization are tools to find factors.

Are there products in geometry?

Yes, calculating area is finding the product of its dimensions.

Can every number be factored?

Every number greater than 1 can be factored into prime numbers, known as its prime factorization.

How does one find the product of two numbers?

By multiplying the numbers together.

Is zero a factor of any number?

Zero is not a factor of any number; however, any number is a factor of zero.

What is the difference between a factor and a multiple?

A factor goes into a number, a multiple is a result of multiplying the number.

Can a product be zero if none of the factors are zero?

No, if the product of numbers is zero, at least one of the factors must be zero.

Why is understanding products important in everyday life?

Understanding products is essential for budgeting, cooking measurements, and making purchasing decisions.

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Author Spotlight

Written by
Maham Liaqat
Co-written by
Fiza Rafique
Fiza Rafique is a skilled content writer at AskDifference.com, where she meticulously refines and enhances written pieces. Drawing from her vast editorial expertise, Fiza ensures clarity, accuracy, and precision in every article. Passionate about language, she continually seeks to elevate the quality of content for readers worldwide.

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