Breaking a number into its building blocks
The factors of a number are the whole numbers that divide it exactly. A prime factorisation writes the number as a product of primes, which is like its unique fingerprint.
Enter any whole number up to a thousand trillion and this calculator lists all its factors and factor pairs, gives the prime factorisation, counts the factors, adds them up and tells you whether the number is prime.
How it is calculated
Divide by 2, 3, 5, 7 … until nothing is left
Number of factors = (e₁ + 1)(e₂ + 1)… for exponents e
Worked example
360
- Prime factorisation
- 2^3 × 3^2 × 5
- Number of factors
- 24
- Sum of factors
- 1170
- Some factors
- 1, 2, 3, 4, 5, 6, 8, 9 …
Quick divisibility tests
| Divisible by | Test |
|---|---|
| 2 | Last digit is even |
| 3 | Digit sum divisible by 3 |
| 5 | Ends in 0 or 5 |
| 9 | Digit sum divisible by 9 |
| 10 | Ends in 0 |
Why 1 is not a prime number
A prime number is defined as having exactly two factors: 1 and itself. The number 1 has only one factor (itself), so it fails that definition and is classed as neither prime nor composite — a special case worth remembering.