Factors and Divisors Calculator
Find all divisors of a whole number, its factor pairs, their sum, and whether the number is prime or perfect.
Tip: If a number has only two divisors (1 and itself), it is prime. Its factor pair is always 1 × the number.
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About this digital tool
The factors (divisors) of a whole number are all the numbers that divide it with no remainder. For example, 36 has 9 divisors: 1, 2, 3, 4, 6, 9, 12, 18 and 36. This tool lists them all, groups them into pairs that multiply to the original number (for example 4 × 9 = 36), adds them up, and tells you whether the number is prime (only two divisors) or perfect (the sum of its divisors, excluding itself, equals the number).
Divisors come up when working with fractions, splitting items into equal groups, planning rows and columns, and in school maths.
How to use
- Enter a positive whole number up to 1,000,000,000,000.
- Read the full list of divisors, from smallest to largest.
- Check the factor pairs and the sum of the divisors.
- Look at the "prime" or "perfect" result at the top of the results.
Frequently asked questions
What are the factors of a number?
Factors (or divisors) are the positive whole numbers that divide the number with no remainder. Every number has at least two factors: 1 and itself.
How do you find the factors of a number?
Try dividing the number by every whole number from 1 up to its square root. Whenever the division leaves no remainder, both numbers in the pair (the divisor and the result) are factors. For 36 the pairs are 1 × 36, 2 × 18, 3 × 12, 4 × 9 and 6 × 6.
What is a perfect number?
A perfect number equals the sum of its divisors, not counting itself. The first examples are 6 (1 + 2 + 3 = 6) and 28 (1 + 2 + 4 + 7 + 14 = 28).
What is the difference between factors and prime factorization?
Factors are all the divisors of a number. Prime factorization breaks the number down into primes only, for example 36 = 2² × 3². The prime factorization tool is under "Prime Numbers".