Divisor vs. Factor: What's the Difference?

By Janet White & Aimie Carlson || Updated on May 22, 2024
A "divisor" is a number that divides another number without leaving a remainder, while a "factor" is a number that, when multiplied with another, produces a given number.

Key Differences

A "divisor" is a number that can divide another number completely, meaning there is no remainder after the division. For example, 3 is a divisor of 9 because 9 divided by 3 equals 3 with no remainder. A "factor," on the other hand, is a number that, when multiplied with another number, results in a given product. For instance, 3 and 3 are factors of 9 because 3 multiplied by 3 equals 9.
When considering divisors, the emphasis is on the division process. If you divide 12 by 4 and get 3 with no remainder, 4 is a divisor of 12. Factors focus on multiplication. For example, 4 and 3 are factors of 12 because 4 times 3 equals 12.
Divisors are always whole numbers that divide another number without leaving a remainder, ensuring the quotient is also a whole number. Factors are pairs of numbers that multiply together to produce a target number. Factors can include both prime and composite numbers.
A divisor is typically discussed in the context of divisibility and division operations, where it simplifies the number into whole parts. Factors are often explored in the context of breaking down numbers into their multiplicative components, useful in various mathematical applications such as prime factorization.

Comparison Chart

Definition

A number that divides another without remainder
A number that, when multiplied with another, produces a given number

Division
Multiplication

Example

3 is a divisor of 9 (9 ÷ 3 = 3)
3 and 3 are factors of 9 (3 × 3 = 9)

Focus

Division process
Multiplication process

Divisibility
Factorization

Divisor and Factor Definitions

Divisor

A number that divides another without leaving a remainder.
5 is a divisor of 20 because 20 ÷ 5 = 4.

Factor

A number that, when multiplied with another, produces a given number.
4 and 5 are factors of 20 because 4 × 5 = 20.

Divisor

A whole number by which another whole number can be divided.
2 is a divisor of 8 because 8 ÷ 2 = 4.

Factor

One of two or more numbers that are multiplied to get a product.
3 and 7 are factors of 21 because 3 × 7 = 21.

Divisor

The number by which the dividend is divided in a division operation.
In 15 ÷ 3 = 5, 3 is the divisor.

Factor

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

Divisor

A number that can be evenly divided into another number.
6 is a divisor of 18 because 18 ÷ 6 = 3.

Factor

One who acts for someone else; an agent.

Divisor

Any integer that divides another integer exactly.
4 is a divisor of 16 because 16 ÷ 4 = 4.

Factor

One who purchases accounts receivable at a discount.

Divisor

The quantity by which another quantity, the dividend, is to be divided.

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.

Divisor

(arithmetic) A number or expression that another is to be divided by.
In "42 ÷ 3" the divisor is the 3.

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.

Divisor

An integer that divides another integer an integral number of times.
The positive divisors of 6 are 1, 2, 3 and 6.

Factor

A gene. No longer in technical usage.

Divisor

The number by which the dividend is divided.

Factor

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

Divisor

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

Factor

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

Divisor

The number by which a dividend is divided

Factor

To engage in purchasing accounts receivable at a discount.

Factor

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

Factor

An agent or representative.

(legal)

Factor

A commission agent.

Factor

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

Factor

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

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.

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.

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.

Factor

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

Factor

(Scotland) A steward or bailiff of an estate.

Factor

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

Factor

To be a product of other objects.

Factor

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

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.

Factor

A steward or bailiff of an estate.

Factor

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

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

An integer that divides another number exactly and leaves no remainder.
2 and 8 are factors of 16 because 2 × 8 = 16.

Factor

A number that is multiplied by another number to yield a product.
6 is a factor of 18 because 6 × 3 = 18.

Factor

A number that is multiplied to form a product with another number.
1, 2, 4, and 8 are factors of 8.

FAQs

Is every factor also a divisor?

Yes, every factor of a number is also a divisor of that number.

Can a divisor be greater than the number itself?

No, a divisor must be less than or equal to the number it divides.

What is a factor?

A factor is a number that, when multiplied with another number, produces a given product.

Can a number have more than two divisors?

Yes, many numbers have multiple divisors. For example, 12 has 1, 2, 3, 4, 6, and 12 as divisors.

How do you find the factors of a number?

To find the factors of a number, identify all pairs of numbers that multiply to give the original number.

What is an example of a divisor?

4 is a divisor of 12 because 12 divided by 4 equals 3 with no remainder.

What is a common divisor?

A common divisor is a number that can divide two or more numbers without leaving a remainder.

What is an example of a factor?

3 and 4 are factors of 12 because 3 multiplied by 4 equals 12.

What is the difference between a prime factor and a divisor?

A prime factor is a prime number that is a factor of a given number, while a divisor can be any number that divides another without remainder.

What is a divisor?

A divisor is a number that divides another number without leaving a remainder.

Are all divisors factors?

Yes, all divisors of a number are also its factors.

How many factors does a prime number have?

A prime number has exactly two factors: 1 and itself.

Is every factor a whole number?

Yes, factors are always whole numbers.

Can zero be a divisor?

No, zero cannot be a divisor as division by zero is undefined.

What does it mean to factor a number?

To factor a number means to break it down into its component factors.

Are 1 and the number itself always factors?

Yes, 1 and the number itself are always factors of any given number.

What are the factors of 36?

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

How do you determine if a number is a divisor of another?

A number is a divisor of another if it divides the other number without leaving a remainder.

What is a common factor?

A common factor is a factor that two or more numbers have in common.

Is 1 considered a divisor?

Yes, 1 is considered a divisor of every number.