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Factors of a number

Enter a whole number and see all its factors, its prime factorisation, how many divisors it has and whether it is prime. It works for numbers up to 1,000,000,000,000.

A positive whole number up to 1,000,000,000,000.

Fill in the fields; the answer appears here straight away.

How it works

  1. Enter the values

    Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.

  2. Instant answer

    The answer appears as you type, with the most important intermediate values.

  3. See the working

    Under "How it's worked out" you see the steps, handy for checking your own calculation.

Factors and prime factors

The factors (or divisors) of a number are the whole numbers that divide it without a remainder. 360 has 24 of them: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 … up to 360.

The prime factorisation writes the number as a product of primes: 360 = 2³ × 3² × 5. Every whole number greater than 1 has exactly one prime factorisation. From it you can find the number of divisors: add 1 to every exponent and multiply, (3 + 1) × (2 + 1) × (1 + 1) = 24.

Prime or not?

A number is prime when it has exactly two divisors: 1 and itself. 2, 3, 5, 7, 11 and 13 are primes; 1 is not. Need the greatest common divisor or least common multiple of several numbers? Use the GCD calculator or the LCM calculator.

Worked example: 360

Divide by 2 until you cannot: 360 → 180 → 90 → 45, which is three 2s. Then by 3: 45 → 15 → 5, two 3s. What remains is 5. So 360 = 2³ × 3² × 5. The factors come in pairs: 1 × 360, 2 × 180, 3 × 120, 4 × 90, 5 × 72, 6 × 60, 8 × 45, 9 × 40, 10 × 36, 12 × 30, 15 × 24 and 18 × 20.

The sum of the divisors

With the factorisation you can also add the divisors without listing them: (1 + 2 + 4 + 8) × (1 + 3 + 9) × (1 + 5) = 15 × 13 × 6 = 1,170. The calculator shows the same total. A number is called perfect when its divisors, without the number itself, add up to the number: 6 (1 + 2 + 3) and 28 are perfect.

What factors are used for

Simplifying fractions, finding the size of equal groups, working out which tile sizes fit a floor, and cryptography (which relies on large numbers being hard to factor). For the common factors of two or more numbers, use the GCD calculator.

Frequently asked questions

How many factors does a number have?

Write it as a product of primes, add 1 to every exponent and multiply. 360 = 2³ × 3² × 5, so it has (3 + 1) × (2 + 1) × (1 + 1) = 24 factors.

How can I tell if a number is prime?

A prime has exactly two divisors, 1 and itself. Enter the number: if the list shows only those two and "Prime? Yes", it is prime. 1 is not prime.

What is a factor pair?

Two factors that multiply to the number, such as 6 × 60 for 360. A number has an odd count of factors only when it is a perfect square: 36 has 9 factors.

What is the largest number I can enter?

Whole numbers up to 1,000,000,000,000 (10^12). Larger values are refused, so the answer stays quick.