Factors are the building blocks of multiplication. Listing them helps you simplify fractions, find common denominators, arrange objects in rectangular arrays and solve number puzzles.
How to use the Factor Calculator
- Number #1
- Number #2 (optional, 0 to skip)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The calculator factorises the number into primes and combines the prime powers to generate every divisor, so even large numbers are handled quickly.
Tips
- Estimate the answer first so you can spot an impossible result.
- Work with whole numbers where possible and place the decimal point at the end.
- Use the order of operations: brackets, powers, multiplication and division, then addition and subtraction.
- For large integers, the calculator works with exact whole-number arithmetic in your browser.
Common mistakes to avoid
- Misaligning decimal points when adding or subtracting.
- Forgetting the remainder in whole-number division.
- Rounding too early in a multi-step calculation.
Formula
d is a factor of n ⇔ n ÷ d leaves no remainderNumber of factors = (e₁ + 1)(e₂ + 1)… for n = p₁^e₁ p₂^e₂ …Worked example
Inputs — Number #1: 36; Number #2 (optional, 0 to skip): 48.
Results — Factors of number #1 = 1, 2, 3, 4, 6, 9, 12, 18, 36; How many factors = 9; Factor pairs = (1, 36) (2, 18) (3, 12) (4, 9) (6, 6); Prime factorisation = 2² × 3²; Factors of number #2 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; Common factors = 1, 2, 3, 4, 6, 12.
Key terms
- Factor (divisor)
- A whole number that divides another exactly.
Frequently asked questions
What are the factors of 36?
1, 2, 3, 4, 6, 9, 12, 18 and 36.
What is a factor pair?
Two numbers that multiply to give the number, such as (4, 9) for 36.
Which numbers have an odd number of factors?
Perfect squares, because one factor pair repeats (6 × 6).
Is 1 a factor of every number?
Yes, and every number is a factor of itself.
What formula does the Factor Calculator use?
d is a factor of n ⇔ n ÷ d leaves no remainder.