What is a factor pair?

A factor pair is two numbers that multiply together to produce the original number, such as 4 and 9 for 36 (4 × 9 = 36).

How is prime factorization different from a factor list?

A factor list shows every number that divides your number evenly. Prime factorization shows only the prime numbers that multiply together to build your number, such as 36 = 2² × 3².

Is there a limit to how large a number I can factor?

The calculator works for typical whole numbers used in schoolwork and everyday math; extremely large numbers may take longer or exceed practical limits.

Math CalculatorsClient-Side Calculation Engine

Factor Calculator

Find all factors, factor pairs, and prime factors.

Math Calculators

Factor Calculator

Find all integer factors, factor pairs, and prime factorization for any given positive integer.

Enter Positive Integer

All Factors (9)

1, 2, 3, 4, 6, 9, 12, 18, 36

Factor Pairs: (1 × 36) (2 × 18) (3 × 12) (4 × 9) (6 × 6)

What is the Factor Calculator and How Does It Work?

The Factor Calculator finds every positive integer that divides a given number evenly, pairs those factors together, and breaks the number down into its prime factorization.

Calculation Formula

Factors of n = every integer d where n ÷ d has no remainder

The calculator tests every whole number from 1 up to n to find which ones divide n with no remainder, pairing each factor with its complement (d and n/d).

Where:

n= The number being factored

d= A candidate divisor being tested against n

Worked Calculation Examples

Factors of 36

Input:36

Output:1, 2, 3, 4, 6, 9, 12, 18, 36

Factor pairs: (1,36), (2,18), (3,12), (4,9), (6,6). Prime factorization: 2² × 3².

Factors of a Prime Number

Input:29

Output:1, 29

Since 29 is prime, its only factors are 1 and itself.

Common Real-World Use Cases

Simplifying Fractions

Find shared factors between a numerator and denominator to reduce a fraction to lowest terms.

Finding GCF and LCM by Hand

List out all factors of two numbers as a manual cross-check against the GCF/LCM calculators.

Arranging Items in Grids

Find all the ways a quantity of items can be arranged evenly into rows and columns.

How to Use the Factor Calculator

1Enter a positive integer.
2The calculator finds every factor pair that multiplies to your number.
3View the full factor list and the prime factorization.

Pro Tips & Suggestions

•Every number has at least two factors: 1 and itself.
•A number with exactly two factors (1 and itself) is prime - check the Prime Number Checker to confirm.

Frequently Asked Questions

Explore Category

Math Calculators

Essential mathematical calculators for fractions, algebra, formulas, and general math.

View All Category Tools

Related Calculators & Tools

mathLIVE

Prime Number Checker

Check whether an integer is prime or composite and view its complete factor list and prime factorization.

Instant calculationReady →

mathLIVE

Greatest Common Factor (GCF) Calculator

Find the greatest common factor (GCF / HCF) of two or more numbers using prime factorization or Euclidean algorithm.

Instant calculationReady →

mathLIVE

Least Common Multiple (LCM) Calculator

Find the least common multiple (LCM) of two or more numbers with step-by-step formula and prime factor breakdown.

Instant calculationReady →

mathLIVE

Fraction Calculator

Add, subtract, multiply, and divide fractions, mixed numbers, and decimals with step-by-step simplification and visual fraction inputs.

Instant calculationReady →

mathLIVE

Average (Mean) Calculator

Calculate the arithmetic mean, sum, count, minimum, maximum, and range of any set of numbers.

Instant calculationReady →

mathLIVE

Median Calculator

Find the middle number (median), mode, range, and sorted numerical sequence of any set of data.

Instant calculationReady →