A factor (or divisor) of a number is any whole number that divides it evenly with no remainder.
About this calculator
A factor (or divisor) of a number is any whole number that divides it evenly with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each divides 12 exactly. Knowing factors helps with simplifying fractions, finding the GCF and LCM, checking divisibility rules, and spotting prime numbers.
This calculator lists every factor of your input, shows factor pairs that multiply to the number, counts how many divisors exist, and tells you whether the number is prime. Enter any integer from the homework range up to one million — negative inputs use the absolute value for factor listing.
Factor pairs are useful when you split a number into two sides of a rectangle or when you factorise quadratics. If a number has only two factors, it is prime. For related tools use the [[gcf]] calculator for greatest common factor, the [[lcm]] calculator for least common multiple, and the [[prime-factorization]] calculator to break a number into prime powers.
Common uses
- List all factors for school maths homework
- Check if a number is prime before cryptography or puzzles
- Find factor pairs when factorising expressions
- Prepare inputs for GCF and LCM calculations
Frequently asked questions
What are the factors of 36?
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. There are nine factors in total. Factor pairs are (1,36), (2,18), (3,12), (4,9), and (6,6).
How do you find all factors of a number quickly?
Test every integer from 1 up to the square root of the number. Whenever the division has no remainder, record both the divisor and the matching quotient. Sort the list at the end.
What is the difference between factors and multiples?
Factors divide into the number evenly. Multiples are numbers the original divides into — for 6, factors are 1, 2, 3, 6 while multiples are 6, 12, 18, and so on.
How many factors does a prime number have?
A prime number has exactly two factors: 1 and itself. For example, 17 is prime because only 1 and 17 divide it with no remainder.