About the Factor Calculator
A factor, or divisor, of a number divides it exactly with no remainder. The factors of 12 are 1, 2, 3, 4, 6 and 12. Finding them by hand means testing divisors one by one, which is slow for big numbers. This factor calculator lists every factor of any whole number up to one trillion, groups them into factor pairs, writes the prime factorisation, counts the factors and adds them up. It also tells you whether the number is prime, meaning it has exactly two factors, or perfect, meaning its factors other than itself add up to the number. It is useful for school maths, simplifying fractions and puzzles.
Updated October 2026
How to use the Factor Calculator
- 1Type a whole number.
- 2Read the full list of factors in the result.
- 3Look at the prime factorisation and the number of factors.
- 4Check the factor pairs.
- 5Note whether the number is prime or perfect.
Worked example: 360
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360, which is 24 factors. The prime factorisation is 2³ × 3² × 5. The sum of all factors is 1,170. Because 360 has so many factors, it is a favourite for dividing a circle: 360 degrees can be split evenly in many ways.
A nice pattern to notice is that perfect squares have an odd number of factors, because one factor pair is made of two equal numbers and is only counted once. 36 has nine factors and 49 has three. Numbers with many small prime factors, such as 60, 120 and 360, are called highly composite and are popular for measuring systems, which is why we have 60 minutes in an hour and 360 degrees in a circle. Try a few numbers in the calculator and look at the pattern in the factor counts.
Quick divisibility tests
- Divisible by 2 if the last digit is even.
- Divisible by 3 if the digit sum is divisible by 3.
- Divisible by 5 if it ends in 0 or 5.
- Divisible by 9 if the digit sum is divisible by 9.
- Divisible by 11 if the alternating digit sum is divisible by 11.
Uses
Factors help you simplify fractions, find common denominators, split items into equal groups, tile floors with whole tiles and arrange seating. In cryptography, the difficulty of factoring very large numbers is what keeps some encryption secure, although that involves numbers far bigger than this tool handles.
Related tools
The GCF and LCM Calculator finds common factors and multiples of several numbers, the Prime Number Calculator checks primes and lists them, the Simplify Fraction Calculator uses factors to reduce fractions and the Long Division Calculator shows working.
Features
- All factors in order
- Factor pairs
- Prime factorisation with exponents
- Count and sum of factors
- Detects prime and perfect numbers
- Works up to one trillion
Frequently asked questions
What are the factors of a number?
They are the whole numbers that divide it exactly. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Every number has 1 and itself as factors.
What is a factor pair?
Two factors that multiply to give the number. For 36 the pairs are 1×36, 2×18, 3×12, 4×9 and 6×6. Listing the pairs is a quick way to be sure you have found all the factors.
What is prime factorisation?
It writes a number as a product of prime numbers. 360 = 2³ × 3² × 5. Every whole number above 1 has exactly one such factorisation, a result known as the fundamental theorem of arithmetic.
How can I tell if a number is prime?
A prime number has exactly two factors, 1 and itself. If the factor list has more than two entries, the number is composite. 13 has factors 1 and 13 only, so it is prime.
How many factors does a number have?
Add one to each exponent in the prime factorisation and multiply the results. For 360 = 2³ × 3² × 5¹ that is 4 × 3 × 2 = 24 factors.
What is a perfect number?
A number equal to the sum of its factors other than itself. 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14 are perfect. The next ones are 496 and 8,128.