712×3π9÷24√5+36∞=48∑17−100Δ11∫2≈152³×3²84×6=2460GCF45LCM144prime1312=2²×3721,2,3,6HCF²³factor188132252×3×56×8=4850divisor

Factor Calculator

Find all factors, prime factorization, factor pairs, and factor tree of any number — instantly.

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The Factor Calculator above finds every factor of any whole number up to one trillion, along with its prime factorization, factor pairs, and a visual factor tree — all instantly. A factor is any whole number that divides another number exactly, with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Type any number above to see its factors, or read on to learn how to find factors yourself step-by-step.

What is a factor?

A factor of a number is a whole number that divides it exactly, leaving no remainder. Factors are the building blocks of multiplication — for any given number, its factors are the values you can multiply together to make it.

For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these divides 12 evenly:

12 ÷ 1 = 12
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 4 = 3
12 ÷ 6 = 2
12 ÷ 12 = 1

Every whole number greater than 1 has at least two factors: 1 and the number itself. Numbers with exactly two factors are called prime numbers (like 7, 11, 13), while numbers with more than two factors are called composite numbers (like 4, 6, 12).

In math, factors are also called divisors — the two terms mean the same thing when we're talking about whole numbers.

How to find the factors of a number

There are four common ways to find the factors of a number. Each method works for any positive integer, but some are faster for large numbers. You can try them all in the calculator above.

Method 1 — Division method

The division method is the most direct way to find factors: divide the number by every whole number from 1 upward, and record every divisor that gives a remainder of 0.

Example: Finding the factors of 18.

18 ÷ 1 = 18 ✓
18 ÷ 2 = 9 ✓
18 ÷ 3 = 6 ✓
18 ÷ 4 = 4.5 ✗
18 ÷ 5 = 3.6 ✗
18 ÷ 6 = 3 ✓
18 ÷ 9 = 2 ✓
18 ÷ 18 = 1 ✓

Factors of 18: 1, 2, 3, 6, 9, 18.

Shortcut: You only need to check up to the square root of the number. For 18, the square root is about 4.24, so testing 1 through 4 is enough — every factor above √18 pairs with one below it.

Method 2 — Prime factorization

Prime factorization breaks a number down into a product of prime numbers. To do this, keep dividing by the smallest prime that divides the number, until you reach 1.

Example: Prime factorization of 72.

72 ÷ 2 = 36
36 ÷ 2 = 18
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

Prime factors: 2 × 2 × 2 × 3 × 3, or in exponent form: 2³ × 3². This form is unique for every number — no other combination of primes multiplies to 72.

Prime factorization is the foundation of many math topics, including the greatest common factor (GCF), least common multiple (LCM), and cryptography.

Method 3 — Factor pairs

A factor pair is two numbers that multiply to give the original number. Listing factor pairs is a fast way to write down all factors at once.

Example: Factor pairs of 24.

1 × 24 = 24
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24

Combining both sides: 1, 2, 3, 4, 6, 8, 12, 24 — the eight factors of 24. Perfect squares like 36 have a middle pair where both numbers are the same (6 × 6 = 36).

Method 4 — Factor tree

A factor tree is a visual way to see prime factorization. You start with the number at the top, split it into two factors, then keep splitting each composite factor until every leaf is prime.

Example: Factor tree of 36.

36 splits into 2 × 18
18 splits into 2 × 9
9 splits into 3 × 3

The prime leaves are 2, 2, 3, 3 — giving 36 = 2² × 3². The calculator above draws a factor tree automatically for any composite number.

Factors vs multiples vs prime factors

These three terms are related but mean different things. This table summarizes the difference using the number 12 as an example.

Term	Meaning	Example (for 12)
Factor	A whole number that divides the given number exactly.	1, 2, 3, 4, 6, 12
Prime factor	A factor that is also a prime number.	2, 3
Multiple	A number obtained by multiplying the given number by an integer.	12, 24, 36, 48, 60, …
Divisor	Another word for factor (used in the same way).	1, 2, 3, 4, 6, 12

Rule of thumb: factors are always less than or equal to the number; multiples are always greater than or equal to it.

Types of numbers based on their factors

Numbers can be classified by how many factors they have and how those factors add up. The calculator above shows all of these properties automatically for any input.

Type	Definition	Examples
Prime	Exactly two factors: 1 and itself.	2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Composite	More than two factors.	4, 6, 8, 9, 10, 12, 14, 15, 16, 18
Perfect	The sum of its proper factors equals the number itself. Very rare.	6, 28, 496, 8128
Abundant	The sum of its proper factors is greater than the number.	12, 18, 20, 24, 30, 36
Deficient	The sum of its proper factors is less than the number.	1, 2, 3, 4, 5, 7, 8, 9, 10, 11
Perfect square	Product of an integer with itself.	1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Perfect cube	Product of an integer with itself three times.	1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Why do we need factors? Real-world uses

Finding factors of a number isn't just a classroom exercise — it's used in many practical fields. Here are the most common applications.

Simplifying fractions: Dividing the numerator and denominator by their greatest common factor gives the fraction in simplest form. For example, 18/24 simplifies to 3/4 by dividing both by their GCF (6).
Least common multiple (LCM): Used to add or subtract fractions with different denominators, and to solve scheduling problems (e.g., two events repeating every N and M days).
Cryptography: Modern encryption like RSA depends on the difficulty of finding the prime factors of very large numbers. Prime factorization is the foundation of digital security.
Divisibility problems: Testing whether one number divides another, which is used in everything from computer science to accounting.
Grouping and arrangement: If you have 24 items and want to arrange them into equal rows, the factors of 24 tell you all the possible row/column combinations: 1×24, 2×12, 3×8, 4×6.
Algebra and number theory: Factoring is the foundation for solving equations, understanding modular arithmetic, and studying number patterns.

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Divisor Calculator

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References

Definitions and mathematical properties used on this page follow standard references:

Frequently Asked Questions

What is a factor of a number?

A factor of a number is a whole number that divides it exactly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 — because 12 can be divided evenly by each of these numbers. Every whole number greater than 1 has at least two factors: 1 and itself.

How do you find the factors of a number?

To find the factors of a number, divide it by every whole number from 1 up to its square root. If the division has no remainder, both the divisor and the quotient are factors. For example, for 36: 1×36, 2×18, 3×12, 4×9, and 6×6 — so its factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. This is called the trial division method, and it works for any positive integer.

What is a factor pair?

A factor pair is two whole numbers that multiply together to give a specific number. For example, the factor pairs of 24 are (1, 24), (2, 12), (3, 8), and (4, 6) — each pair multiplies to 24. Every number has at least one factor pair (1 × the number itself). Perfect squares like 36 have an extra middle pair where both numbers are the same, such as (6, 6).

How do I figure out the factors of a number quickly?

The fastest way is to check divisibility by small primes first: 2, 3, 5, 7, 11. Only check up to the square root of the number — every factor above the square root has a matching factor below it. For example, to find factors of 100, you only need to test 1 through 10; the factors above 10 (like 20, 25, 50, 100) are found automatically as pairs. This reduces work dramatically for large numbers.

What is factorization of a number?

Factorization is the process of breaking a number down into a product of smaller numbers, usually its factors or prime factors. For example, the factorization of 12 can be written as 2 × 6, 3 × 4, or in prime form as 2 × 2 × 3 (or 2² × 3). Prime factorization is unique for every number — this is called the Fundamental Theorem of Arithmetic.

How do you calculate prime factors?

To calculate prime factors, repeatedly divide the number by the smallest prime that divides it, until you reach 1. For example, for 60: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, 5 ÷ 5 = 1. The prime factors are 2, 2, 3, 5 — written in exponent form as 2² × 3 × 5. This method is called the division method or ladder method.

What is the difference between factors and multiples?

A factor divides a number evenly, while a multiple is the result of multiplying a number by an integer. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 (numbers that divide 12), while the multiples of 12 are 12, 24, 36, 48, 60, and so on (numbers you get by multiplying 12 by 1, 2, 3, 4, 5, ...). Factors are always less than or equal to the number; multiples are always greater than or equal to it.

Can a negative number be a factor?

Yes, mathematically every positive integer has both positive and negative factors. For example, the factors of 12 include −1, −2, −3, −4, −6, −12 in addition to 1, 2, 3, 4, 6, 12. However, in everyday math, school, and most calculators (including this one), only positive factors are listed by default, because they cover every meaningful divisor without duplication.

What multiplies to give a number?

The pairs of whole numbers that multiply to give a specific number are called its factor pairs. For example, numbers that multiply to give 24 are: 1 × 24, 2 × 12, 3 × 8, and 4 × 6. To find these for any number, you list its factors and pair each factor with its matching quotient. Every whole number has at least one such pair.

How do you find all the factors of a number in one go?

The most efficient method is to loop through every integer from 1 to the square root of the number. Each time you find a divisor with no remainder, add both the divisor and its quotient to your list. Finally, sort the list. For example, for 72, you check 1, 2, 3, 4, 5, 6, 7, 8 — the divisors are 1, 2, 3, 4, 6, 8 and their pairs are 72, 36, 24, 18, 12, 9. Combined and sorted: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 — exactly 12 factors.

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

A factor is any whole number that divides another number exactly. A prime factor is a factor that is also a prime number — meaning it can only be divided by 1 and itself. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, but only 2 and 3 are prime factors. Every composite number can be expressed as a product of its prime factors in exactly one way.

What are common factors and the greatest common factor (GCF)?

Common factors are numbers that divide two or more given numbers exactly. The greatest common factor (GCF), also called HCF, is the largest of these common factors. For example, the common factors of 12 and 18 are 1, 2, 3, and 6 — so their GCF is 6. The GCF is useful for simplifying fractions and solving problems involving grouping.

What is a factor in math versus a factor in algebra?

In basic math, a factor is a whole number that divides another whole number exactly, like 3 being a factor of 12. In algebra, a factor is any expression that multiplies with others to form a bigger expression — for example, (x + 2) and (x − 2) are factors of x² − 4. This calculator focuses on number factors (arithmetic factoring), not algebraic expression factoring.

Why do we need to find factors of a number?

Finding factors is used in many real-world and academic tasks: simplifying fractions, finding the greatest common factor (GCF) and least common multiple (LCM), solving divisibility problems, grouping items evenly, cryptography (RSA relies on prime factorization), and scheduling problems. Understanding factors is a foundation for algebra, number theory, and computer science.

What are the smallest and largest factors of any number?

The smallest factor of any positive whole number is always 1, and the largest factor is always the number itself. For example, for 100 the smallest factor is 1 and the largest is 100. Between these two, other factors exist depending on whether the number is prime (only 1 and itself) or composite (has additional factors in between).